set.seed (1996 ) library (tidyverse)
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library (dplyr)library (ggplot2)library (rstan)
Loading required package: StanHeaders
rstan version 2.32.5 (Stan version 2.32.2)
For execution on a local, multicore CPU with excess RAM we recommend calling
options(mc.cores = parallel::detectCores()).
To avoid recompilation of unchanged Stan programs, we recommend calling
rstan_options(auto_write = TRUE)
For within-chain threading using `reduce_sum()` or `map_rect()` Stan functions,
change `threads_per_chain` option:
rstan_options(threads_per_chain = 1)
Attaching package: 'rstan'
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Loading required package: Rcpp
This is rstanarm version 2.32.1
- See https://mc-stan.org/rstanarm/articles/priors for changes to default priors!
- Default priors may change, so it's safest to specify priors, even if equivalent to the defaults.
- For execution on a local, multicore CPU with excess RAM we recommend calling
options(mc.cores = parallel::detectCores())
Attaching package: 'rstanarm'
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This is cmdstanr version 0.6.1
- CmdStanR documentation and vignettes: mc-stan.org/cmdstanr
- CmdStan path: /Users/sofiagerard/.cmdstan/cmdstan-2.33.1
- CmdStan version: 2.33.1
A newer version of CmdStan is available. See ?install_cmdstan() to install it.
To disable this check set option or environment variable CMDSTANR_NO_VER_CHECK=TRUE.
This is rstantools version 2.3.1.1
library (nleqslv)library (bayesplot)
This is bayesplot version 1.10.0
- Online documentation and vignettes at mc-stan.org/bayesplot
- bayesplot theme set to bayesplot::theme_default()
* Does _not_ affect other ggplot2 plots
* See ?bayesplot_theme_set for details on theme setting
Attaching package: 'coda'
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Ejercicio 1:
La expectativa de \(X\) se calcula como:
\[
E[X] = \frac{\alpha}{\alpha + \beta} = 0.6
\]
Lo que nos lleva a la relación entre \(\alpha\) y \(\beta\) :
\[
0.4\alpha = 0.6\beta
\]
\[
\frac{2}{3}\alpha = \beta
\]
La varianza de \(X\) está dada por:
\[
\text{var}[X] = \frac{\alpha\beta}{(\alpha + \beta)^2(\alpha + \beta + 1)} = 0.042^2
\]
Desarrollando la ecuación, obtenemos:
\[
\left(\frac{2}{3}\alpha\right)^2\left(\frac{5}{3}\alpha + 1\right) = 0.042^2
\]
\[
\frac{2}{3}\alpha^2 = (0.042)^2\left(\frac{5}{3^2}\alpha^2\right)\left(\frac{5}{3}\alpha + 1\right)
\]
\[
\frac{2}{3}\alpha^2 = (0.042)^2\left(\frac{5^3}{3^3}\alpha^3 + \frac{5^2}{3^2}\alpha\right)
\]
\[
\frac{2}{3}\alpha^2 = 0.042^2\left(\frac{5^3}{3^3}\alpha^3\right)
\]
Finalmente, asumiendo que \(\alpha \neq 0\) :
\[
\alpha = \frac{\frac{2}{3} - (0.042)^2\left(\frac{5^2}{3^2}\right)}{0.042^2\left(\frac{5^3}{3^3}\right)} \approx 89.4
\]
\[
\beta = \frac{2}{3}\alpha \approx 59.6
\]
# μ = α / (α + β) # σ² = αβ / ((α + β)²(α + β + 1)) # Datos dados <- 0.60 # Tasa promedio <- 0.04 # Desviación estándar # Calcular la varianza <- sigma^ 2 # Calcular los parámetros alpha y beta usando las fórmulas <- (mu * (1 - mu) / variance - 1 ) * mu<- alpha * (1 / mu - 1 )# Mostrar los valores de alpha y beta print (paste ("Alpha:" , alpha))print (paste ("Beta:" , beta))# Graficar la distribución Beta curve (dbeta (x, shape1 = alpha, shape2 = beta), from = 0 , to = 1 , main = "Distribución Beta" , xlab = "x" , ylab = "Densidad" ,col = "blue" )
Inciso b
# Distribución Normal transformada para conocimiento inicial = mu# Graficar la distribución normal <- seq (0 , 1 , length.out = 100 )<- dnorm (x, mean = mean, sd = sqrt (variance))plot (x, y, type = "l" , col = "blue" , lwd = 2 , main = paste ("Distribución normal(" , mean, "," , variance, ")" ),xlab = "x" , ylab = "Densidad de probabilidad" )
Inciso c
# Inicial de referencia no informativa para theta <- seq (0 , 1 , length.out = 100 )<- rep (1 , 100 )plot (x, y, type = "l" , col = "blue" , lwd = 2 , main = expression (paste (theta, " Unif(0,1)" )),xlab = "x" , ylab = "Densidad de probabilidad" )
Inciso d
# Modelo a # Datos del año 2024 <- list (solicitados = 100 , otorgados = 50 )# Distribución inicial del inciso (a) - Distribución Beta # Parámetros alpha y beta iniciales <- 89.40 <- 59.60 # Combinar datos y parámetros iniciales en una lista para Stan <- list (solicitados = datos$ solicitados, otorgados = datos$ otorgados, alpha_prior = alpha_prior, beta_prior = beta_prior)# Especifica la ruta del archivo Stan <- "Ej1-modeloa.stan" # Compilar el modelo Stan desde el archivo <- stan_model (file = ruta_archivo_stan1)# Ejecutar el modelo Stan <- sampling (modelo_stan1, data = datos_stan1, chains = 4 , iter = 10000 )
SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
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# Resumen de los resultados print (summary (resultados_stan1))
$summary
mean se_mean sd 2.5% 25% 50%
theta 0.5598829 0.0003611676 0.03130911 0.4981931 0.53871 0.5600657
lp__ -171.3044964 0.0076512481 0.71141617 -173.3049855 -171.46481 -171.0312931
75% 97.5% n_eff Rhat
theta 0.5809936 0.6209651 7514.914 1.000267
lp__ -170.8562856 -170.8066965 8645.356 1.000627
$c_summary
, , chains = chain:1
stats
parameter mean sd 2.5% 25% 50%
theta 0.5607619 0.03179211 0.4987833 0.5390875 0.560951
lp__ -171.3208836 0.72764263 -173.3505710 -171.4853208 -171.041632
stats
parameter 75% 97.5%
theta 0.5819671 0.6237532
lp__ -170.8592865 -170.8066313
, , chains = chain:2
stats
parameter mean sd 2.5% 25% 50%
theta 0.559288 0.03114069 0.4976092 0.5385063 0.5598339
lp__ -171.299152 0.72579921 -173.3817487 -171.4551154 -171.0229267
stats
parameter 75% 97.5%
theta 0.5797235 0.619474
lp__ -170.8520292 -170.806719
, , chains = chain:3
stats
parameter mean sd 2.5% 25% 50%
theta 0.5592326 0.03197512 0.4967433 0.5376002 0.5593093
lp__ -171.3256502 0.73574812 -173.3263187 -171.5041545 -171.0483142
stats
parameter 75% 97.5%
theta 0.5811719 0.6191967
lp__ -170.8615480 -170.8068330
, , chains = chain:4
stats
parameter mean sd 2.5% 25% 50%
theta 0.5602492 0.03028295 0.50042 0.5396215 0.5604194
lp__ -171.2722995 0.65222727 -173.11986 -171.4200041 -171.0174413
stats
parameter 75% 97.5%
theta 0.5804281 0.619498
lp__ -170.8527325 -170.806685
# Extraer muestras de theta <- extract (resultados_stan1)$ theta# Graficar las posteriores de theta hist (muestras_theta1, breaks = 30 , main = "Posterior de theta con Beta" , xlab = "theta" , ylab = "Densidad" , col = "skyblue" )
# Modelo b # Datos del año 2024 <- list (solicitados = 100 , otorgados = 50 )# Distribución inicial del inciso (b) - Distribución Normal Modificada (0.6, 0.0016) # Parámetros mu y sigma iniciales <- 0.6 <- 0.0016 # Combinar datos y parámetros iniciales en una lista para Stan <- list (solicitados = datos$ solicitados, otorgados = datos$ otorgados, mu_prior = mu_prior, sigma_prior = sigma_prior)# Especifica la ruta del archivo Stan <- "Ej1-modelob.stan" # Compilar el modelo Stan desde el archivo <- stan_model (file = ruta_archivo_stan2)# Ejecutar el modelo Stan <- sampling (modelo_stan2, data = datos_stan2, chains = 4 , iter = 10000 )
SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
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# Resumen de los resultados print (summary (resultados_stan2))
$summary
mean se_mean sd 2.5% 25% 50%
theta 0.5999044 1.858194e-05 0.001604577 0.5967629 0.5988209 0.5999162
lp__ -73.2840901 7.540486e-03 0.713098208 -75.2580460 -73.4497374 -73.0114587
75% 97.5% n_eff Rhat
theta 0.6009945 0.6030125 7456.567 1.000517
lp__ -72.8299809 -72.7810659 8943.345 1.000366
$c_summary
, , chains = chain:1
stats
parameter mean sd 2.5% 25% 50%
theta 0.5999072 0.001638477 0.5966747 0.5988086 0.5999372
lp__ -73.3055247 0.731494202 -75.3929810 -73.4877893 -73.0239844
stats
parameter 75% 97.5%
theta 0.6010357 0.6030397
lp__ -72.8310545 -72.7810623
, , chains = chain:2
stats
parameter mean sd 2.5% 25% 50%
theta 0.5998994 0.001571018 0.5968814 0.5988038 0.5999179
lp__ -73.2631595 0.683538838 -75.0658158 -73.4058264 -73.0137665
stats
parameter 75% 97.5%
theta 0.6009871 0.6029137
lp__ -72.8312244 -72.7813010
, , chains = chain:3
stats
parameter mean sd 2.5% 25% 50%
theta 0.5998817 0.001587269 0.5967369 0.5988433 0.5998721
lp__ -73.2731992 0.701342742 -75.2317999 -73.4383469 -72.9963051
stats
parameter 75% 97.5%
theta 0.6009482 0.6029712
lp__ -72.8272974 -72.7811285
, , chains = chain:4
stats
parameter mean sd 2.5% 25% 50%
theta 0.5999293 0.001620776 0.596818 0.5988242 0.5999311
lp__ -73.2944772 0.734184152 -75.308599 -73.4610650 -73.0153321
stats
parameter 75% 97.5%
theta 0.6010125 0.6031474
lp__ -72.8308732 -72.7809904
# Extraer muestras de theta <- extract (resultados_stan2)$ theta# Graficar las posteriores de theta hist (muestras_theta2, breaks = 30 , main = "Posterior de theta con Normal Transformada" , xlab = "theta" , ylab = "Densidad" , col = "skyblue" )
# Modelo c # Datos del año 2024 <- list (solicitados = 100 , otorgados = 50 )# Distribución inicial del inciso (c) - Distribución Uniforme (0,1) # No hay parámetros a especificar # Combinar datos y parámetros iniciales en una lista para Stan <- list (solicitados = datos$ solicitados, otorgados = datos$ otorgados)# Especifica la ruta del archivo Stan <- "Ej1-modeloc.stan" # Compilar el modelo Stan desde el archivo <- stan_model (file = ruta_archivo_stan3)# Ejecutar el modelo Stan <- sampling (modelo_stan3, data = datos_stan3, chains = 4 , iter = 10000 )
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# Resumen de los resultados print (summary (resultados_stan3))
$summary
mean se_mean sd 2.5% 25% 50%
theta 0.499545 0.0005974795 0.04931517 0.4025504 0.4663421 0.4996972
lp__ -71.204568 0.0070474395 0.71776763 -73.2821281 -71.3653693 -70.9285404
75% 97.5% n_eff Rhat
theta 0.5330038 0.5958356 6812.633 1.000191
lp__ -70.7519200 -70.7015819 10373.015 1.000513
$c_summary
, , chains = chain:1
stats
parameter mean sd 2.5% 25% 50%
theta 0.4998134 0.04937365 0.4043552 0.4661258 0.4997827
lp__ -71.2056950 0.72136797 -73.2794547 -71.3608275 -70.9338826
stats
parameter 75% 97.5%
theta 0.5335305 0.5948625
lp__ -70.7517115 -70.7016349
, , chains = chain:2
stats
parameter mean sd 2.5% 25% 50% 75%
theta 0.498337 0.04890992 0.4024369 0.4654035 0.4969119 0.5314679
lp__ -71.196688 0.70811197 -73.1852727 -71.3504298 -70.9266392 -70.7511517
stats
parameter 97.5%
theta 0.5961156
lp__ -70.7015177
, , chains = chain:3
stats
parameter mean sd 2.5% 25% 50%
theta 0.4996124 0.05083224 0.3992545 0.4659888 0.5002172
lp__ -71.2363706 0.75902185 -73.4831978 -71.4066412 -70.9361689
stats
parameter 75% 97.5%
theta 0.5337623 0.5983788
lp__ -70.7545958 -70.7015887
, , chains = chain:4
stats
parameter mean sd 2.5% 25% 50% 75%
theta 0.5004172 0.04809626 0.4051361 0.467568 0.5018179 0.5331045
lp__ -71.1795196 0.67930821 -73.0381466 -71.330156 -70.9198070 -70.7500391
stats
parameter 97.5%
theta 0.5931362
lp__ -70.7016026
# Extraer muestras de theta <- extract (resultados_stan3)$ theta# Graficar las posteriores de theta plot (density (muestras_theta3), main = expression (paste (theta, " Unif(0,1)" )), xlab = "theta" , ylab = "Densidad de probabilidad" , col = "blue" )
Inciso e
# Cargar las muestras de theta obtenidas en los tres modelos <- extract (resultados_stan1)$ theta<- extract (resultados_stan2)$ theta<- extract (resultados_stan3)$ theta# Calcular la media de las distribuciones posteriores de theta <- mean (muestras_theta_a)<- mean (muestras_theta_b)<- mean (muestras_theta_c)# Imprimir los resultados cat ("Estimación de la tasa de créditos otorgados usando las tres distribuciones finales: \n " )
Estimación de la tasa de créditos otorgados usando las tres distribuciones finales:
cat ("Inciso (a):" , theta_media_a, " \n " )cat ("Inciso (b):" , theta_media_b, " \n " )cat ("Inciso (c):" , theta_media_c, " \n " )
Inciso f
# Calcular el momio de otorgar un crédito utilizando las medias de las distribuciones finales phi = theta / ( 1 - theta ) # Calcular el momio de otorgar un crédito utilizando las medias de las distribuciones finales <- theta_media_a / (1 - theta_media_a)<- theta_media_b / (1 - theta_media_b)<- theta_media_c / (1 - theta_media_c)# Imprimir los resultados cat ("Momio de otorgar un crédito usando las medias de las distribuciones finales: \n " )
Momio de otorgar un crédito usando las medias de las distribuciones finales:
cat ("Inciso (a):" , phi_a, " \n " )cat ("Inciso (b):" , phi_b, " \n " )cat ("Inciso (c):" , phi_c, " \n " )
Ejercicio 2:
Inciso a
# Datos de las utilidades mensuales ( # verosimilitud normal(mu, sigma**2)) <- c (212 , 207 , 210 , 196 , 223 , 193 , 196 , 210 , 202 , 221 )<- length (utilidades)<- 200 <- 40 <- 10 <- 1 # Combinar datos <- list (N = N, utilidades = utilidades, prior_mu_mean = prior_mu_mean,prior_mu_var = prior_mu_var, prior_sigma_shape = prior_sigma_shape,prior_sigma_rate = prior_sigma_rate)# Especifica la ruta del archivo Stan <- "Ej2-incisoa.stan" # Compilar el modelo Stan desde el archivo <- stan_model (file = ruta_archivo_stan4)# Ejecutar el modelo Stan <- sampling (modelo_stan4, data = datos_stan4, chains = 4 , iter = 10000 )
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# Resumen de los resultados print (summary (resultados_stan4))
$summary
mean se_mean sd 2.5% 25% 50% 75%
mu 206.58937 0.01141248 1.5150467 203.59573 205.57734 206.59619 207.60470
sigma_sq 25.07786 0.02891196 3.7621536 18.45737 22.44228 24.80871 27.44168
lp__ -29.61774 0.01038145 0.9873313 -32.24928 -29.99509 -29.31475 -28.91718
97.5% n_eff Rhat
mu 209.54510 17623.492 1.000027
sigma_sq 33.11755 16932.377 1.000192
lp__ -28.65707 9045.028 1.000144
$c_summary
, , chains = chain:1
stats
parameter mean sd 2.5% 25% 50% 75% 97.5%
mu 206.58505 1.533864 203.58492 205.55961 206.60433 207.59984 209.58726
sigma_sq 25.19974 3.764402 18.64220 22.59846 24.89956 27.53531 33.18217
lp__ -29.62632 1.002601 -32.30337 -30.02783 -29.30814 -28.90827 -28.65584
, , chains = chain:2
stats
parameter mean sd 2.5% 25% 50% 75%
mu 206.57971 1.4887469 203.70879 205.58220 206.58556 207.57146
sigma_sq 25.01310 3.7944075 18.17156 22.33619 24.79967 27.35597
lp__ -29.61518 0.9782762 -32.29914 -29.98818 -29.31543 -28.91377
stats
parameter 97.5%
mu 209.49029
sigma_sq 33.03935
lp__ -28.65794
, , chains = chain:3
stats
parameter mean sd 2.5% 25% 50% 75%
mu 206.61926 1.5123890 203.67483 205.56780 206.60594 207.64032
sigma_sq 25.01095 3.6820833 18.61904 22.40115 24.71958 27.41786
lp__ -29.59839 0.9528304 -32.10497 -29.97532 -29.31344 -28.92564
stats
parameter 97.5%
mu 209.59236
sigma_sq 32.93128
lp__ -28.65900
, , chains = chain:4
stats
parameter mean sd 2.5% 25% 50% 75% 97.5%
mu 206.57346 1.524847 203.50972 205.59221 206.58998 207.59893 209.49150
sigma_sq 25.08766 3.804481 18.38593 22.43717 24.78116 27.43791 33.20457
lp__ -29.63105 1.014458 -32.31226 -29.99280 -29.32007 -28.92158 -28.65780
# Graficar la posterior de mu mcmc_trace (resultados_stan4, pars = "mu" )# Graficar la posterior de sigma_sq mcmc_trace (resultados_stan4, pars = "sigma_sq" )# Graficar la posterior conjunta de mu y sigma_sq mcmc_scatter (resultados_stan4, pars = c ("mu" , "sigma_sq" ))# Extracción de los valores de los parámetros <- extract (resultados_stan4)<- parametros$ mu<- parametros$ sigma_sq# Cálculo de las medias <- mean (mu_values)<- mean (sigma_sq_values)# Impresión de los valores cat ("El valor de mu es:" , mu_mean, " \n " )
El valor de mu es: 206.5894
cat ("El valor de sigma^2 es:" , sigma_sq_mean, " \n " )
El valor de sigma^2 es: 25.07786
Inciso b
# Utilizando inicial no informativa para la varianza # Datos de utilidades mensuales <- c (212 , 207 , 210 , 196 , 223 , 193 , 196 , 210 , 202 , 221 )<- length (utilidades)# Combinar datos sin priors específicos <- list (N = N, utilidades = utilidades)# Especifica la ruta del archivo Stan (ajustado para usar sigma_sq) <- "Ej2-incisob.stan" # Compilar y ejecutar el modelo Stan corregido <- stan_model (file = ruta_archivo_stan5)<- sampling (modelo_stan5, data = datos_stan5, chains = 4 , iter = 10000 )
SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
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# Resumen de los resultados print (summary (resultados_stan5))
$summary
mean se_mean sd 2.5% 25% 50% 75%
mu 207.0057 0.03763518 3.690594 199.66754 204.74255 206.97898 209.28297
sigma_sq 135.1401 0.95432791 86.666495 49.93882 83.72312 113.94764 160.13667
lp__ -28.9007 0.01368885 1.101877 -31.86297 -29.31035 -28.56861 -28.12121
97.5% n_eff Rhat
mu 214.45405 9616.221 0.9999943
sigma_sq 346.49443 8247.213 1.0001971
lp__ -27.84221 6479.363 1.0000766
$c_summary
, , chains = chain:1
stats
parameter mean sd 2.5% 25% 50% 75%
mu 206.95883 3.767067 199.34856 204.66046 206.92303 209.25183
sigma_sq 136.04220 96.887322 50.05420 84.30949 113.84379 158.76778
lp__ -28.91296 1.137032 -31.97877 -29.34305 -28.56059 -28.10505
stats
parameter 97.5%
mu 214.64139
sigma_sq 349.11952
lp__ -27.84329
, , chains = chain:2
stats
parameter mean sd 2.5% 25% 50% 75%
mu 207.03019 3.686229 199.62631 204.79351 207.03043 209.32669
sigma_sq 135.30496 83.202092 51.19694 83.37687 113.58939 161.01209
lp__ -28.90741 1.107897 -31.93801 -29.30793 -28.56861 -28.12401
stats
parameter 97.5%
mu 214.30488
sigma_sq 353.13950
lp__ -27.84101
, , chains = chain:3
stats
parameter mean sd 2.5% 25% 50% 75% 97.5%
mu 207.07533 3.632349 200.10771 204.78983 207.0283 209.33080 214.37594
sigma_sq 135.38524 86.179246 48.66956 83.59309 114.7512 161.63194 345.93132
lp__ -28.90289 1.094525 -31.80353 -29.31364 -28.5811 -28.13745 -27.84501
, , chains = chain:4
stats
parameter mean sd 2.5% 25% 50% 75%
mu 206.95841 3.675212 199.58881 204.71761 206.94238 209.23013
sigma_sq 133.82805 79.433028 49.86485 83.36060 113.80612 159.25967
lp__ -28.87952 1.066935 -31.78863 -29.28854 -28.55998 -28.12236
stats
parameter 97.5%
mu 214.46867
sigma_sq 329.97595
lp__ -27.84049
# Extracción de los valores de los parámetros del modelo ajustado <- extract (resultados_stan5)<- parametros_ajustados$ mu<- parametros_ajustados$ sigma_sq# Cálculo de las medias para el modelo ajustado <- mean (mu_values_ajustados)<- mean (sigma_sq_values_ajustados)# Impresión de los valores para el modelo ajustado cat ("El valor de mu es:" , mu_mean_ajustado, " \n " )
El valor de mu es: 207.0057
cat ("El valor de sigma^2 es:" , sigma_sq_mean_ajustado, " \n " )
El valor de sigma^2 es: 135.1401
Ejercicio 3:
Paso 1: Datos
<- read.table ("data/calificaciones.txt" , header = TRUE , sep = "" )
Paso 2 : Ver datos
# Gráfica de dispersión con curva de regresión ggplot (calificaciones, aes (x = MO, y = SP)) + geom_point () + geom_smooth (method = "lm" , col = "red" ) + labs (title = "Relación entre Calificaciones de Moody’s y S&P" ,x = "Calificaciones de Moody’s" , y = "Calificaciones de S&P" ) + theme_minimal ()
`geom_smooth()` using formula = 'y ~ x'
Paso 3: Modelo Stan
<- list (N = nrow (calificaciones),x = calificaciones$ MO,y = calificaciones$ SP)<- "Ej3-modelo.stan" # Compilar y ejecutar el modelo Stan <- stan_model (file = ruta_modelo_calificaciones)<- sampling (modelo_stan_calif, data = datos_stan_calif, chains = 4 , iter = 10000 , warmup = 1000 )
SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
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print (resultados_stan_calif)
Inference for Stan model: anon_model.
4 chains, each with iter=10000; warmup=1000; thin=1;
post-warmup draws per chain=9000, total post-warmup draws=36000.
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
alpha -1.69 0.01 0.78 -3.24 -2.21 -1.69 -1.19 -0.16 9855 1
beta 0.84 0.00 0.16 0.53 0.74 0.84 0.94 1.15 9810 1
sigma 0.47 0.00 0.09 0.34 0.41 0.46 0.52 0.67 12572 1
lp__ 5.20 0.01 1.31 1.79 4.61 5.54 6.15 6.69 9274 1
Samples were drawn using NUTS(diag_e) at Sun Mar 17 13:32:27 2024.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at
convergence, Rhat=1).
summary (resultados_stan_calif)
$summary
mean se_mean sd 2.5% 25% 50%
alpha -1.6943932 0.0078868179 0.78292550 -3.2415869 -2.2070529 -1.6905531
beta 0.8387735 0.0015672368 0.15523125 0.5329658 0.7378265 0.8383906
sigma 0.4683418 0.0007621465 0.08545492 0.3351405 0.4074590 0.4576057
lp__ 5.1985083 0.0136434596 1.31387509 1.7942519 4.6123226 5.5361051
75% 97.5% n_eff Rhat
alpha -1.1864690 -0.1550034 9854.560 1.000072
beta 0.9401311 1.1456687 9810.453 1.000052
sigma 0.5159615 0.6667653 12571.793 1.000148
lp__ 6.1505404 6.6895371 9273.830 1.000620
$c_summary
, , chains = chain:1
stats
parameter mean sd 2.5% 25% 50% 75%
alpha -1.6944900 0.77048711 -3.2243775 -2.2042787 -1.6860629 -1.1700933
beta 0.8385956 0.15270028 0.5466828 0.7343877 0.8379365 0.9388276
sigma 0.4674214 0.08458237 0.3337725 0.4078786 0.4577880 0.5157258
lp__ 5.2007596 1.31075804 1.7914751 4.6150289 5.5404856 6.1432890
stats
parameter 97.5%
alpha -0.2360018
beta 1.1413636
sigma 0.6616661
lp__ 6.6887697
, , chains = chain:2
stats
parameter mean sd 2.5% 25% 50% 75%
alpha -1.7033840 0.7786718 -3.2290929 -2.2129776 -1.7061346 -1.2081469
beta 0.8406582 0.1545700 0.5268109 0.7425579 0.8408845 0.9429514
sigma 0.4688428 0.0846442 0.3347941 0.4082883 0.4589355 0.5167946
lp__ 5.2279670 1.2948281 1.8856178 4.6578586 5.5609634 6.1639931
stats
parameter 97.5%
alpha -0.1263879
beta 1.1456729
sigma 0.6654307
lp__ 6.6888366
, , chains = chain:3
stats
parameter mean sd 2.5% 25% 50% 75%
alpha -1.6887255 0.80532434 -3.2617026 -2.2222136 -1.6864496 -1.1743004
beta 0.8380354 0.15925291 0.5258965 0.7360263 0.8380061 0.9428287
sigma 0.4684143 0.08526311 0.3350406 0.4073257 0.4576315 0.5150687
lp__ 5.1541205 1.33801376 1.6616202 4.5440349 5.4994034 6.1405086
stats
parameter 97.5%
alpha -0.09619505
beta 1.14824944
sigma 0.66858330
lp__ 6.68718619
, , chains = chain:4
stats
parameter mean sd 2.5% 25% 50% 75%
alpha -1.6909732 0.77681509 -3.2476584 -2.1809000 -1.6810615 -1.1927843
beta 0.8378047 0.15433464 0.5359377 0.7379582 0.8362941 0.9359853
sigma 0.4686885 0.08730847 0.3366558 0.4061326 0.4555864 0.5163916
lp__ 5.2111860 1.31060863 1.8419849 4.6293295 5.5445768 6.1509453
stats
parameter 97.5%
alpha -0.1752109
beta 1.1466815
sigma 0.6726441
lp__ 6.6924969
Paso 4: Gráficas e Interpretación
# Graficar la traza de las muestras para verificar la convergencia mcmc_trace (resultados_stan_calif, pars = c ("alpha" , "beta" , "sigma" ))# Graficar las densidades posteriores para las estimaciones de los parámetros mcmc_dens (resultados_stan_calif, pars = c ("alpha" , "beta" , "sigma" ))# Graficar los intervalos de credibilidad para los parámetros mcmc_intervals (resultados_stan_calif, pars = c ("alpha" , "beta" , "sigma" ))# Graficar la distribución posterior conjunta para 'alpha', 'beta', y 'sigma' mcmc_pairs (resultados_stan_calif, pars = c ("alpha" , "beta" , "sigma" ))
Interpretación de los parámetros:
Alpha: La estimación para la intersección (alpha) es de aproximadamente -1.70, con un intervalo de credibilidad del 95% entre -3.26 y -0.15. Esto sugiere que, en promedio, cuando la calificación de Moody’s es cero, la calificación de S&P tiende a estar entre -3.26 y -0.15. La desviación estándar asociada a esta estimación es de aproximadamente 0.78, lo cual muestra la variabilidad e incertidumbre de la estimación.
Beta: La estimación para la pendiente (beta) es de aproximadamente 0.84, con un intervalo de credibilidad del 95% entre 0.54 y 1.15. Esto indica que, en promedio, por cada aumento unitario en la calificación de Moody’s, la calificación de S&P tiende a aumentar entre 0.54 y 1.15 unidades. La desviación estándar asociada a esta estimación es de aproximadamente 0.15.
Sigma: La desviación estándar del término de error (sigma) tiene una estimación de aproximadamente 0.47, con un intervalo de credibilidad del 95% entre 0.34 y 0.66. Esto indica la dispersión de los errores en las predicciones del modelo. La desviación estándar asociada a esta estimación es de aproximadamente 0.08.
Diagnósticos de convergencia:
Los diagnósticos de convergencia (n_eff y Rhat) muestran valores adecuados para todos los parámetros, lo que indica una buena convergencia del modelo.
En resumen, este análisis bayesiano proporciona estimaciones precisas para los parámetros del modelo de regresión lineal, lo que nos permite entender la relación entre las calificaciones de Moody’s y S&P en el contexto de las calificaciones de 20 empresas financieras. Los resultados respaldan la idea inicial de una asociación estadísticamente significativa y positiva entre las calificaciones de ambas compañías calificadoras.
Predicciones posteriores:
# Generar predicciones posteriores manualmente porque no me funciona posterior_predict() # Convertir el objeto stanfit a un data frame <- as.data.frame (extract (resultados_stan_calif))# Definir el número de muestras y el número de observaciones en los datos <- nrow (muestras_df)<- datos_stan_calif$ N# Inicializar un vector para almacenar las predicciones posteriores <- numeric (length = num_muestras * num_observaciones)# Calcular las predicciones posteriores para cada muestra for (i in 1 : num_muestras) {<- muestras_df[i, "alpha" ]<- muestras_df[i, "beta" ]<- muestras_df[i, "sigma" ]# Calcular las predicciones posteriores usando los parámetros muestreados <- rnorm (n = num_observaciones, mean = alpha + beta * datos_stan_calif$ x, sd = sigma)# Almacenar las predicciones en el vector predicciones_posteriores - 1 ) * num_observaciones + 1 ): (i * num_observaciones)] <- predicciones# Crear un histograma de las predicciones posteriores hist (predicciones_posteriores, main = "Predicciones Posteriores" , xlab = "Calificaciones de S&P" , ylab = "Frecuencia" , col = "lightblue" )# Agregar unas líneas vertical para los datos observados abline (v = datos_stan_calif$ y, col = "red" , lwd = 2 )
<- extract (resultados_stan_calif)<- length (calificaciones$ SP) # Número de observaciones <- dim (samples$ alpha)[1 ] # Número de muestras en la cadena MCMC <- matrix (NA , nrow = n_obs, ncol = n_samples) # Matriz para almacenar predicciones for (i in 1 : n_samples) {<- samples$ alpha[i] + $ beta[i] * calificaciones$ MO<- apply (yrep, 1 , mean)if (length (calificaciones$ SP) == length (predicciones_media)) {# Primero crea el gráfico de dispersión plot (calificaciones$ SP, predicciones_media,xlab = "Valores Observados" ,ylab = "Media de Valores Predichos" ,main = "PPC: Valores Observados vs. Media de Valores Predichos" )# Luego, añade la línea roja usando abline() abline (a = 0 , b = 1 , col = "red" )else {stop ("La longitud de los datos observados y las predicciones no coincide." )
El gráfico ilustra la comparación entre las calificaciones observadas y las predicciones generadas por el modelo. Se observan varias desviaciones entre los datos reales y las predicciones del modelo, lo que indica que existen áreas donde el modelo podría ser mejorado para lograr una mayor precisión en sus predicciones.
Ejercicio 4:
Parte 1: Datos
# Y = salario en miles de usd # X1 = el índice de calidad de trabajo # X2 = número de años de experiencia # X3 = índice de éxito en publicaciones <- read.table ("data/salarios.txt" , header = TRUE , sep = "" , dec = "." )# Gráfico de dispersión de Y vs X1 ggplot (salarios, aes (x = X1, y = Y)) + geom_point () + labs (title = "Gráfico de dispersión de Salarios vs Calidad de Trabajo" , x = "Índice de Calidad de Trabajo (X1)" , y = "Salario Anual (Y)" )# Gráfico de dispersión de Y vs X2 ggplot (salarios, aes (x = X2, y = Y)) + geom_point () + labs (title = "Gráfico de dispersión de Salarios vs Años de Experiencia" , x = "Número de Años de Experiencia (X2)" , y = "Salario Anual (Y)" )# Gráfico de dispersión de Y vs X3 ggplot (salarios, aes (x = X3, y = Y)) + geom_point () + labs (title = "Gráfico de dispersión de Salarios vs Índice de Éxito en Publicaciones" , x = "Índice de Éxito en Publicaciones (X3)" , y = "Salario Anual (Y)" )
Parte 2: Modelo
<- list (N = nrow (salarios),X1 = salarios$ X1,X2 = salarios$ X2,X3 = salarios$ X3,Y = salarios$ Y,N_new = 5 ,X1_new = c (5 , 4 , 17 , 6 , 0 ),X2_new = c (6 , 2 , 12 , 5 , 8 ),X3_new = c (6 , 4 , 21 , 6 , 1 ))<- stan_model (file = "Ej4-modelo.stan" )<- sampling (modelo_salarios, data = datos_salarios, iter = 10000 , chains = 4 )
SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
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print (ajuste_salarios, pars = c ("alpha" , "beta1" , "beta2" , "beta3" , "sigma" ))
Inference for Stan model: anon_model.
4 chains, each with iter=10000; warmup=5000; thin=1;
post-warmup draws per chain=5000, total post-warmup draws=20000.
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
alpha 17.11 0.02 2.09 12.87 15.75 17.15 18.48 21.09 9766 1
beta1 1.16 0.00 0.35 0.48 0.94 1.16 1.39 1.86 10711 1
beta2 0.32 0.00 0.04 0.24 0.30 0.32 0.35 0.40 12307 1
beta3 1.36 0.00 0.31 0.75 1.15 1.35 1.56 1.99 11048 1
sigma 1.84 0.00 0.31 1.35 1.62 1.80 2.01 2.53 10956 1
Samples were drawn using NUTS(diag_e) at Sun Mar 17 13:33:12 2024.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at
convergence, Rhat=1).
<- extract (ajuste_salarios)$ salary_pred
Parte 3: Interpretación y Gráficas
alpha
beta1
beta2
beta3
sigma
Los valores de n_effRhat
mcmc_hist (ajuste_salarios, pars = c ("alpha" , "beta1" , "beta2" , "beta3" , "sigma" ))
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
ggplot (salarios, aes (x = X1, y = Y)) + geom_point () + geom_smooth (method = "lm" , formula = y ~ x, se = TRUE ) + labs (title = "Gráfico de dispersión de Salarios vs Calidad de Trabajo con Línea de Regresión" ,x = "Índice de Calidad de Trabajo (X1)" , y = "Salario Anual (Y)" )ggplot (salarios, aes (x = X2, y = Y)) + geom_point () + geom_smooth (method = "lm" , formula = y ~ x, se = TRUE ) + labs (title = "Gráfico de dispersión de Salarios vs Años de Experiencia" ,x = "Añps de Experiencia (X2)" , y = "Salario Anual (Y)" )ggplot (salarios, aes (x = X3, y = Y)) + geom_point () + geom_smooth (method = "lm" , formula = y ~ x, se = TRUE ) + labs (title = "Gráfico de dispersión de Salarios vs Índice de Éxito en Publicaciones con Línea de Regresión" ,x = "Índice de Éxito en Publicaciones (X3)" , y = "Salario Anual (Y)" )mcmc_dens_overlay (ajuste_salarios)
# Chequeos predictivos posteriores (PPC) # Generar predicciones posteriores manualmente porque no me funciona posterior_predict() # Extraer las muestras de los parámetros del modelo <- extract (ajuste_salarios)# Asumiendo que tus nombres de parámetros son 'alpha', 'beta1', 'beta2', 'beta3' y 'sigma' # Genera predicciones posteriores para cada observación <- length (salarios$ Y) # Número de observaciones <- dim (samples$ alpha)[1 ] # Número de muestras en la cadena MCMC <- matrix (NA , nrow = n_obs, ncol = n_samples) # Matriz para almacenar predicciones for (i in 1 : n_samples) {<- samples$ alpha[i] + $ beta1[i] * salarios$ X1 + $ beta2[i] * salarios$ X2 + $ beta3[i] * salarios$ X3# Ahora 'yrep' contiene las predicciones posteriores # Calcular la media de las predicciones <- apply (yrep, 1 , mean)# Asegúrate de que 'salarios$Y' y 'predicciones_media' tienen la misma longitud if (length (salarios$ Y) == length (predicciones_media)) {# Primero crea el gráfico de dispersión plot (salarios$ Y, predicciones_media,xlab = "Valores Observados" ,ylab = "Media de Valores Predichos" ,main = "PPC: Valores Observados vs. Media de Valores Predichos" )# Luego, añade la línea roja usando abline() abline (a = 0 , b = 1 , col = "red" )else {stop ("La longitud de los datos observados y las predicciones no coincide." )
El gráfico muestra cómo se comparan los salarios observados con las predicciones del modelo. La mayoría de los puntos están cerca de la línea roja, lo que indica una buena concordancia entre los valores observados y predichos. Sin embargo, hay algunas desviaciones, lo que sugiere que el modelo podría mejorarse en ciertas áreas.
Ejercicio 5:
Parte 1:
Datos y modelo logit binomial :
# pii = probabilidad de muerte # xi = tiempo de exposición al mineral # yi = número de muertes # varianza = 1/precisión # Como vimos en clase, en este ejercicio b0 y b1 estan en terminos de precision y no de varianza por lo que bi~ N(mu = 0, precisión = 0.001) -> en términos de varianza sería bi~ N(mu=0, 1000 ) # La relación entre la probabilidad de muerte y el tiempo de exposición se modela a través de la función logit que es el logaritmo de las odds (probabilidad de que ocurra el evento dividido por la probabilidad de que no ocurra): logit(pii) = log( pii / 1 - pii ) = b0 + b1*xi # Leer los datos <- read.table ("data/mortality.txt" , header = TRUE , sep = "" )# Prepara los datos para Stan, incluyendo nuevos datos para predicción <- list (N = nrow (datos_mortality),y = datos_mortality$ y,n = datos_mortality$ n,x = as.vector (datos_mortality$ x),new_N = 100 , new_x = 200 , new_n = rep (1 , 100 )# Ajusta el modelo con los datos <- stan (file = "Ej5-modelo1.stan" , data = stan_data_mortality, iter = 10000 , chains = 4 )
SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
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Chain 3: 0.207 seconds (Total)
Chain 3:
SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
Chain 4:
Chain 4: Gradient evaluation took 3e-06 seconds
Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.03 seconds.
Chain 4: Adjust your expectations accordingly!
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Chain 4:
# Ver un resumen de los resultados print (fit_mortality)
Inference for Stan model: anon_model.
4 chains, each with iter=10000; warmup=5000; thin=1;
post-warmup draws per chain=5000, total post-warmup draws=20000.
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff
alpha -3.59 0.00 0.21 -4.02 -3.73 -3.58 -3.44 -3.19 5751
beta 0.01 0.00 0.00 0.01 0.01 0.01 0.01 0.01 6974
y_pred[1] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19296
y_pred[2] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20360
y_pred[3] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19765
y_pred[4] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19427
y_pred[5] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20050
y_pred[6] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20491
y_pred[7] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19710
y_pred[8] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19466
y_pred[9] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19835
y_pred[10] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19497
y_pred[11] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 19994
y_pred[12] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19750
y_pred[13] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 18696
y_pred[14] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19791
y_pred[15] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 19998
y_pred[16] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20687
y_pred[17] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20117
y_pred[18] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20465
y_pred[19] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19458
y_pred[20] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19848
y_pred[21] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19882
y_pred[22] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19218
y_pred[23] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19694
y_pred[24] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20422
y_pred[25] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20345
y_pred[26] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 18845
y_pred[27] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 19571
y_pred[28] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20136
y_pred[29] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19200
y_pred[30] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19940
y_pred[31] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19224
y_pred[32] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20433
y_pred[33] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19998
y_pred[34] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 18866
y_pred[35] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 19428
y_pred[36] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 20663
y_pred[37] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19763
y_pred[38] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 18746
y_pred[39] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20221
y_pred[40] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19816
y_pred[41] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19417
y_pred[42] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 20117
y_pred[43] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19742
y_pred[44] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19996
y_pred[45] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 18936
y_pred[46] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20742
y_pred[47] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19817
y_pred[48] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 19481
y_pred[49] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19442
y_pred[50] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20189
y_pred[51] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19779
y_pred[52] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20040
y_pred[53] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19680
y_pred[54] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20330
y_pred[55] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 20108
y_pred[56] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19863
y_pred[57] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 19738
y_pred[58] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 19415
y_pred[59] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19556
y_pred[60] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20009
y_pred[61] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19881
y_pred[62] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19975
y_pred[63] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 20108
y_pred[64] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19905
y_pred[65] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19592
y_pred[66] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 19453
y_pred[67] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20336
y_pred[68] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 20192
y_pred[69] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19899
y_pred[70] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19581
y_pred[71] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 19772
y_pred[72] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 19783
y_pred[73] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20388
y_pred[74] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 19021
y_pred[75] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 19686
y_pred[76] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20304
y_pred[77] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19836
y_pred[78] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 18803
y_pred[79] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 18920
y_pred[80] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 19925
y_pred[81] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 19359
y_pred[82] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19716
y_pred[83] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 18928
y_pred[84] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20543
y_pred[85] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19772
y_pred[86] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20092
y_pred[87] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20408
y_pred[88] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20215
y_pred[89] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20412
y_pred[90] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20349
y_pred[91] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19321
y_pred[92] 0.22 0.00 0.41 0.00 0.00 0.00 0.00 1.00 19668
y_pred[93] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20096
y_pred[94] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20289
y_pred[95] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19414
y_pred[96] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 18347
y_pred[97] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20628
y_pred[98] 0.23 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19708
y_pred[99] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 19711
y_pred[100] 0.22 0.00 0.42 0.00 0.00 0.00 0.00 1.00 20377
lp__ -161.08 0.01 0.98 -163.70 -161.46 -160.78 -160.38 -160.11 7559
Rhat
alpha 1
beta 1
y_pred[1] 1
y_pred[2] 1
y_pred[3] 1
y_pred[4] 1
y_pred[5] 1
y_pred[6] 1
y_pred[7] 1
y_pred[8] 1
y_pred[9] 1
y_pred[10] 1
y_pred[11] 1
y_pred[12] 1
y_pred[13] 1
y_pred[14] 1
y_pred[15] 1
y_pred[16] 1
y_pred[17] 1
y_pred[18] 1
y_pred[19] 1
y_pred[20] 1
y_pred[21] 1
y_pred[22] 1
y_pred[23] 1
y_pred[24] 1
y_pred[25] 1
y_pred[26] 1
y_pred[27] 1
y_pred[28] 1
y_pred[29] 1
y_pred[30] 1
y_pred[31] 1
y_pred[32] 1
y_pred[33] 1
y_pred[34] 1
y_pred[35] 1
y_pred[36] 1
y_pred[37] 1
y_pred[38] 1
y_pred[39] 1
y_pred[40] 1
y_pred[41] 1
y_pred[42] 1
y_pred[43] 1
y_pred[44] 1
y_pred[45] 1
y_pred[46] 1
y_pred[47] 1
y_pred[48] 1
y_pred[49] 1
y_pred[50] 1
y_pred[51] 1
y_pred[52] 1
y_pred[53] 1
y_pred[54] 1
y_pred[55] 1
y_pred[56] 1
y_pred[57] 1
y_pred[58] 1
y_pred[59] 1
y_pred[60] 1
y_pred[61] 1
y_pred[62] 1
y_pred[63] 1
y_pred[64] 1
y_pred[65] 1
y_pred[66] 1
y_pred[67] 1
y_pred[68] 1
y_pred[69] 1
y_pred[70] 1
y_pred[71] 1
y_pred[72] 1
y_pred[73] 1
y_pred[74] 1
y_pred[75] 1
y_pred[76] 1
y_pred[77] 1
y_pred[78] 1
y_pred[79] 1
y_pred[80] 1
y_pred[81] 1
y_pred[82] 1
y_pred[83] 1
y_pred[84] 1
y_pred[85] 1
y_pred[86] 1
y_pred[87] 1
y_pred[88] 1
y_pred[89] 1
y_pred[90] 1
y_pred[91] 1
y_pred[92] 1
y_pred[93] 1
y_pred[94] 1
y_pred[95] 1
y_pred[96] 1
y_pred[97] 1
y_pred[98] 1
y_pred[99] 1
y_pred[100] 1
lp__ 1
Samples were drawn using NUTS(diag_e) at Sun Mar 17 13:33:44 2024.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at
convergence, Rhat=1).
$summary
mean se_mean sd 2.5% 25%
alpha -3.587062 2.790530e-03 0.211618651 -4.01755101 -3.72538157
beta 0.011642 1.777302e-05 0.001484183 0.00873104 0.01064694
y_pred[1] 0.226550 3.013499e-03 0.418609435 0.00000000 0.00000000
y_pred[2] 0.222700 2.915931e-03 0.416068943 0.00000000 0.00000000
y_pred[3] 0.221850 2.955422e-03 0.415501155 0.00000000 0.00000000
y_pred[4] 0.221750 2.980554e-03 0.415434191 0.00000000 0.00000000
y_pred[5] 0.221700 2.933649e-03 0.415400696 0.00000000 0.00000000
y_pred[6] 0.222550 2.905887e-03 0.415968928 0.00000000 0.00000000
y_pred[7] 0.225550 2.977073e-03 0.417954461 0.00000000 0.00000000
y_pred[8] 0.222200 2.979732e-03 0.415735254 0.00000000 0.00000000
y_pred[9] 0.227050 2.974620e-03 0.418935643 0.00000000 0.00000000
y_pred[10] 0.223600 2.984031e-03 0.416667398 0.00000000 0.00000000
y_pred[11] 0.220350 2.931343e-03 0.414493025 0.00000000 0.00000000
y_pred[12] 0.225200 2.972360e-03 0.417724412 0.00000000 0.00000000
y_pred[13] 0.222800 3.043370e-03 0.416135577 0.00000000 0.00000000
y_pred[14] 0.222750 2.957787e-03 0.416102265 0.00000000 0.00000000
y_pred[15] 0.219150 2.925286e-03 0.413680836 0.00000000 0.00000000
y_pred[16] 0.224000 2.898764e-03 0.416932479 0.00000000 0.00000000
y_pred[17] 0.224250 2.940743e-03 0.417097873 0.00000000 0.00000000
y_pred[18] 0.226000 2.923647e-03 0.418249622 0.00000000 0.00000000
y_pred[19] 0.222050 2.979645e-03 0.415634978 0.00000000 0.00000000
y_pred[20] 0.221300 2.946665e-03 0.415132421 0.00000000 0.00000000
y_pred[21] 0.226150 2.966899e-03 0.418347856 0.00000000 0.00000000
y_pred[22] 0.224800 3.011337e-03 0.417460985 0.00000000 0.00000000
y_pred[23] 0.225300 2.977107e-03 0.417790184 0.00000000 0.00000000
y_pred[24] 0.221900 2.907789e-03 0.415534624 0.00000000 0.00000000
y_pred[25] 0.223700 2.921647e-03 0.416733720 0.00000000 0.00000000
y_pred[26] 0.223600 3.035247e-03 0.416667398 0.00000000 0.00000000
y_pred[27] 0.219900 2.960648e-03 0.414189048 0.00000000 0.00000000
y_pred[28] 0.222250 2.929952e-03 0.415768662 0.00000000 0.00000000
y_pred[29] 0.226950 3.022948e-03 0.418870469 0.00000000 0.00000000
y_pred[30] 0.222850 2.947180e-03 0.416168881 0.00000000 0.00000000
y_pred[31] 0.223600 3.005152e-03 0.416667398 0.00000000 0.00000000
y_pred[32] 0.226300 2.927336e-03 0.418446012 0.00000000 0.00000000
y_pred[33] 0.225850 2.956940e-03 0.418151312 0.00000000 0.00000000
y_pred[34] 0.222100 3.026303e-03 0.415668412 0.00000000 0.00000000
y_pred[35] 0.220750 2.975648e-03 0.414762630 0.00000000 0.00000000
y_pred[36] 0.220700 2.885168e-03 0.414728960 0.00000000 0.00000000
y_pred[37] 0.225250 2.971664e-03 0.417757302 0.00000000 0.00000000
y_pred[38] 0.221600 3.033517e-03 0.415333679 0.00000000 0.00000000
y_pred[39] 0.227150 2.946549e-03 0.419000782 0.00000000 0.00000000
y_pred[40] 0.222600 2.955187e-03 0.416002275 0.00000000 0.00000000
y_pred[41] 0.224250 2.993309e-03 0.417097873 0.00000000 0.00000000
y_pred[42] 0.219950 2.920504e-03 0.414222859 0.00000000 0.00000000
y_pred[43] 0.225050 2.972302e-03 0.417625691 0.00000000 0.00000000
y_pred[44] 0.224750 2.951933e-03 0.417428018 0.00000000 0.00000000
y_pred[45] 0.225800 3.038499e-03 0.418118525 0.00000000 0.00000000
y_pred[46] 0.222800 2.889392e-03 0.416135577 0.00000000 0.00000000
y_pred[47] 0.224150 2.962428e-03 0.417031741 0.00000000 0.00000000
y_pred[48] 0.218900 2.962691e-03 0.413510991 0.00000000 0.00000000
y_pred[49] 0.224800 2.993988e-03 0.417460985 0.00000000 0.00000000
y_pred[50] 0.226450 2.945649e-03 0.418544091 0.00000000 0.00000000
y_pred[51] 0.221150 2.951101e-03 0.415031674 0.00000000 0.00000000
y_pred[52] 0.221450 2.933195e-03 0.415233089 0.00000000 0.00000000
y_pred[53] 0.224100 2.972537e-03 0.416998662 0.00000000 0.00000000
y_pred[54] 0.226050 2.933566e-03 0.418282375 0.00000000 0.00000000
y_pred[55] 0.220550 2.923994e-03 0.414627897 0.00000000 0.00000000
y_pred[56] 0.221500 2.946476e-03 0.415266628 0.00000000 0.00000000
y_pred[57] 0.221050 2.953622e-03 0.414964465 0.00000000 0.00000000
y_pred[58] 0.217750 2.962057e-03 0.412726852 0.00000000 0.00000000
y_pred[59] 0.230050 3.009651e-03 0.420875105 0.00000000 0.00000000
y_pred[60] 0.226050 2.957008e-03 0.418282375 0.00000000 0.00000000
y_pred[61] 0.222300 2.948953e-03 0.415802062 0.00000000 0.00000000
y_pred[62] 0.228250 2.969724e-03 0.419715077 0.00000000 0.00000000
y_pred[63] 0.220200 2.922335e-03 0.414391778 0.00000000 0.00000000
y_pred[64] 0.224900 2.959416e-03 0.417526893 0.00000000 0.00000000
y_pred[65] 0.221900 2.968686e-03 0.415534624 0.00000000 0.00000000
y_pred[66] 0.220350 2.971855e-03 0.414493025 0.00000000 0.00000000
y_pred[67] 0.227550 2.940024e-03 0.419261000 0.00000000 0.00000000
y_pred[68] 0.218850 2.909803e-03 0.413476995 0.00000000 0.00000000
y_pred[69] 0.223300 2.952348e-03 0.416468225 0.00000000 0.00000000
y_pred[70] 0.221500 2.967637e-03 0.415266628 0.00000000 0.00000000
y_pred[71] 0.218150 2.937145e-03 0.413000128 0.00000000 0.00000000
y_pred[72] 0.217950 2.935334e-03 0.412863561 0.00000000 0.00000000
y_pred[73] 0.221950 2.910391e-03 0.415568084 0.00000000 0.00000000
y_pred[74] 0.218000 2.993783e-03 0.412897716 0.00000000 0.00000000
y_pred[75] 0.218900 2.947174e-03 0.413510991 0.00000000 0.00000000
y_pred[76] 0.227700 2.943023e-03 0.419358442 0.00000000 0.00000000
y_pred[77] 0.223350 2.957240e-03 0.416501442 0.00000000 0.00000000
y_pred[78] 0.222800 3.034714e-03 0.416135577 0.00000000 0.00000000
y_pred[79] 0.227950 3.049939e-03 0.419520676 0.00000000 0.00000000
y_pred[80] 0.220250 2.935911e-03 0.414425536 0.00000000 0.00000000
y_pred[81] 0.219800 2.976396e-03 0.414121401 0.00000000 0.00000000
y_pred[82] 0.224850 2.973309e-03 0.417493943 0.00000000 0.00000000
y_pred[83] 0.219700 3.009583e-03 0.414053719 0.00000000 0.00000000
y_pred[84] 0.226250 2.919262e-03 0.418413302 0.00000000 0.00000000
y_pred[85] 0.222700 2.958971e-03 0.416068943 0.00000000 0.00000000
y_pred[86] 0.227850 2.959218e-03 0.419455808 0.00000000 0.00000000
y_pred[87] 0.226350 2.929340e-03 0.418478714 0.00000000 0.00000000
y_pred[88] 0.226150 2.942412e-03 0.418347856 0.00000000 0.00000000
y_pred[89] 0.226600 2.930203e-03 0.418642094 0.00000000 0.00000000
y_pred[90] 0.224500 2.925102e-03 0.417263053 0.00000000 0.00000000
y_pred[91] 0.225200 3.005192e-03 0.417724412 0.00000000 0.00000000
y_pred[92] 0.220400 2.955762e-03 0.414526756 0.00000000 0.00000000
y_pred[93] 0.229100 2.964594e-03 0.420264228 0.00000000 0.00000000
y_pred[94] 0.222600 2.920557e-03 0.416002275 0.00000000 0.00000000
y_pred[95] 0.225850 3.001070e-03 0.418151312 0.00000000 0.00000000
y_pred[96] 0.227200 3.093590e-03 0.419033339 0.00000000 0.00000000
y_pred[97] 0.222500 2.896002e-03 0.415935572 0.00000000 0.00000000
y_pred[98] 0.226000 2.979310e-03 0.418249622 0.00000000 0.00000000
y_pred[99] 0.221550 2.958056e-03 0.415300158 0.00000000 0.00000000
y_pred[100] 0.224700 2.923998e-03 0.417395042 0.00000000 0.00000000
lp__ -161.075739 1.128568e-02 0.981188895 -163.70037456 -161.46183943
50% 75% 97.5% n_eff Rhat
alpha -3.58016164 -3.44091335 -3.18827752 5750.884 1.0006398
beta 0.01163171 0.01263898 0.01457612 6973.526 1.0006847
y_pred[1] 0.00000000 0.00000000 1.00000000 19296.377 1.0000412
y_pred[2] 0.00000000 0.00000000 1.00000000 20359.923 1.0000807
y_pred[3] 0.00000000 0.00000000 1.00000000 19765.391 0.9999933
y_pred[4] 0.00000000 0.00000000 1.00000000 19427.209 1.0001593
y_pred[5] 0.00000000 0.00000000 1.00000000 20050.169 0.9999270
y_pred[6] 0.00000000 0.00000000 1.00000000 20491.055 0.9999884
y_pred[7] 0.00000000 0.00000000 1.00000000 19709.651 1.0000487
y_pred[8] 0.00000000 0.00000000 1.00000000 19466.117 1.0001787
y_pred[9] 0.00000000 0.00000000 1.00000000 19834.975 1.0001784
y_pred[10] 0.00000000 0.00000000 1.00000000 19497.206 1.0001006
y_pred[11] 0.00000000 0.00000000 1.00000000 19994.074 0.9998529
y_pred[12] 0.00000000 0.00000000 1.00000000 19750.441 0.9999568
y_pred[13] 0.00000000 0.00000000 1.00000000 18696.500 0.9998881
y_pred[14] 0.00000000 0.00000000 1.00000000 19790.933 1.0002295
y_pred[15] 0.00000000 0.00000000 1.00000000 19998.356 0.9998915
y_pred[16] 0.00000000 0.00000000 1.00000000 20687.389 0.9999849
y_pred[17] 0.00000000 0.00000000 1.00000000 20116.940 0.9999143
y_pred[18] 0.00000000 0.00000000 1.00000000 20465.449 0.9999872
y_pred[19] 0.00000000 0.00000000 1.00000000 19457.859 1.0002576
y_pred[20] 0.00000000 0.00000000 1.00000000 19847.779 0.9999770
y_pred[21] 0.00000000 0.00000000 1.00000000 19882.441 0.9999243
y_pred[22] 0.00000000 0.00000000 1.00000000 19218.215 1.0000453
y_pred[23] 0.00000000 0.00000000 1.00000000 19693.711 1.0000728
y_pred[24] 0.00000000 0.00000000 1.00000000 20421.546 0.9998594
y_pred[25] 0.00000000 0.00000000 1.00000000 20345.190 0.9999705
y_pred[26] 0.00000000 0.00000000 1.00000000 18844.781 0.9999422
y_pred[27] 0.00000000 0.00000000 1.00000000 19571.487 0.9998819
y_pred[28] 0.00000000 0.00000000 1.00000000 20136.426 0.9998443
y_pred[29] 0.00000000 0.00000000 1.00000000 19199.859 0.9998944
y_pred[30] 0.00000000 0.00000000 1.00000000 19940.036 0.9999048
y_pred[31] 0.00000000 0.00000000 1.00000000 19224.100 1.0001408
y_pred[32] 0.00000000 0.00000000 1.00000000 20433.079 1.0000329
y_pred[33] 0.00000000 0.00000000 1.00000000 19997.791 0.9998992
y_pred[34] 0.00000000 0.00000000 1.00000000 18865.543 1.0000390
y_pred[35] 0.00000000 0.00000000 1.00000000 19428.362 1.0000225
y_pred[36] 0.00000000 0.00000000 1.00000000 20662.671 0.9998453
y_pred[37] 0.00000000 0.00000000 1.00000000 19762.814 0.9999731
y_pred[38] 0.00000000 0.00000000 1.00000000 18745.692 1.0001568
y_pred[39] 0.00000000 0.00000000 1.00000000 20220.985 1.0000054
y_pred[40] 0.00000000 0.00000000 1.00000000 19816.253 1.0000560
y_pred[41] 0.00000000 0.00000000 1.00000000 19416.582 0.9998961
y_pred[42] 0.00000000 0.00000000 1.00000000 20116.509 0.9998954
y_pred[43] 0.00000000 0.00000000 1.00000000 19741.882 1.0000303
y_pred[44] 0.00000000 0.00000000 1.00000000 19996.325 1.0000106
y_pred[45] 0.00000000 0.00000000 1.00000000 18935.671 1.0000720
y_pred[46] 0.00000000 0.00000000 1.00000000 20742.296 0.9998825
y_pred[47] 0.00000000 0.00000000 1.00000000 19817.214 1.0001269
y_pred[48] 0.00000000 0.00000000 1.00000000 19480.564 0.9999453
y_pred[49] 0.00000000 0.00000000 1.00000000 19441.587 1.0000188
y_pred[50] 0.00000000 0.00000000 1.00000000 20189.265 1.0000579
y_pred[51] 0.00000000 0.00000000 1.00000000 19778.544 0.9999151
y_pred[52] 0.00000000 0.00000000 1.00000000 20040.200 0.9999538
y_pred[53] 0.00000000 0.00000000 1.00000000 19679.531 1.0000351
y_pred[54] 0.00000000 0.00000000 1.00000000 20330.474 0.9999845
y_pred[55] 0.00000000 0.00000000 1.00000000 20107.772 0.9999216
y_pred[56] 0.00000000 0.00000000 1.00000000 19863.154 0.9999342
y_pred[57] 0.00000000 0.00000000 1.00000000 19738.402 0.9999275
y_pred[58] 0.00000000 0.00000000 1.00000000 19415.056 0.9999101
y_pred[59] 0.00000000 0.00000000 1.00000000 19555.739 1.0001095
y_pred[60] 0.00000000 0.00000000 1.00000000 20009.397 0.9999273
y_pred[61] 0.00000000 0.00000000 1.00000000 19880.969 1.0002213
y_pred[62] 0.00000000 0.00000000 1.00000000 19974.543 0.9999934
y_pred[63] 0.00000000 0.00000000 1.00000000 20107.692 1.0000200
y_pred[64] 0.00000000 0.00000000 1.00000000 19904.760 1.0000138
y_pred[65] 0.00000000 0.00000000 1.00000000 19592.326 0.9999626
y_pred[66] 0.00000000 0.00000000 1.00000000 19452.671 0.9999312
y_pred[67] 0.00000000 0.00000000 1.00000000 20336.077 1.0002064
y_pred[68] 0.00000000 0.00000000 1.00000000 20191.829 0.9999700
y_pred[69] 0.00000000 0.00000000 1.00000000 19898.886 0.9999392
y_pred[70] 0.00000000 0.00000000 1.00000000 19580.891 0.9999528
y_pred[71] 0.00000000 0.00000000 1.00000000 19771.954 0.9999052
y_pred[72] 0.00000000 0.00000000 1.00000000 19783.274 1.0002751
y_pred[73] 0.00000000 0.00000000 1.00000000 20388.330 1.0000656
y_pred[74] 0.00000000 0.00000000 1.00000000 19021.477 0.9999869
y_pred[75] 0.00000000 0.00000000 1.00000000 19686.226 1.0000014
y_pred[76] 0.00000000 0.00000000 1.00000000 20304.093 0.9999671
y_pred[77] 0.00000000 0.00000000 1.00000000 19836.266 1.0001289
y_pred[78] 0.00000000 0.00000000 1.00000000 18803.304 0.9998945
y_pred[79] 0.00000000 0.00000000 1.00000000 18920.139 1.0001145
y_pred[80] 0.00000000 0.00000000 1.00000000 19925.413 1.0000852
y_pred[81] 0.00000000 0.00000000 1.00000000 19358.603 0.9999709
y_pred[82] 0.00000000 0.00000000 1.00000000 19716.067 0.9999484
y_pred[83] 0.00000000 0.00000000 1.00000000 18927.824 0.9999589
y_pred[84] 0.00000000 0.00000000 1.00000000 20543.042 0.9999693
y_pred[85] 0.00000000 0.00000000 1.00000000 19771.931 0.9998786
y_pred[86] 0.00000000 0.00000000 1.00000000 20091.787 0.9999365
y_pred[87] 0.00000000 0.00000000 1.00000000 20408.323 0.9999951
y_pred[88] 0.00000000 0.00000000 1.00000000 20214.733 0.9999517
y_pred[89] 0.00000000 0.00000000 1.00000000 20412.227 1.0001653
y_pred[90] 0.00000000 0.00000000 1.00000000 20348.755 0.9999953
y_pred[91] 0.00000000 0.00000000 1.00000000 19321.254 0.9998834
y_pred[92] 0.00000000 0.00000000 1.00000000 19668.269 0.9999769
y_pred[93] 0.00000000 0.00000000 1.00000000 20096.223 1.0000091
y_pred[94] 0.00000000 0.00000000 1.00000000 20288.974 0.9999947
y_pred[95] 0.00000000 0.00000000 1.00000000 19413.986 1.0001549
y_pred[96] 0.00000000 0.00000000 1.00000000 18347.284 1.0000757
y_pred[97] 0.00000000 0.00000000 1.00000000 20627.864 1.0000744
y_pred[98] 0.00000000 0.00000000 1.00000000 19707.867 0.9999999
y_pred[99] 0.00000000 0.00000000 1.00000000 19711.128 1.0001849
y_pred[100] 0.00000000 0.00000000 1.00000000 20377.010 0.9999297
lp__ -160.77633141 -160.37609324 -160.11098308 7558.740 1.0009859
$c_summary
, , chains = chain:1
stats
parameter mean sd 2.5% 25%
alpha -3.58664955 0.209291032 -4.022928e+00 -3.71895642
beta 0.01164196 0.001485002 8.686007e-03 0.01066523
y_pred[1] 0.23020000 0.421002861 0.000000e+00 0.00000000
y_pred[2] 0.21520000 0.411002122 0.000000e+00 0.00000000
y_pred[3] 0.22440000 0.417228302 0.000000e+00 0.00000000
y_pred[4] 0.22420000 0.417096097 0.000000e+00 0.00000000
y_pred[5] 0.22200000 0.415632711 0.000000e+00 0.00000000
y_pred[6] 0.23140000 0.421769627 0.000000e+00 0.00000000
y_pred[7] 0.22460000 0.417360369 0.000000e+00 0.00000000
y_pred[8] 0.22580000 0.418149889 0.000000e+00 0.00000000
y_pred[9] 0.21340000 0.409748726 0.000000e+00 0.00000000
y_pred[10] 0.23200000 0.422151208 0.000000e+00 0.00000000
y_pred[11] 0.21720000 0.412381100 0.000000e+00 0.00000000
y_pred[12] 0.23000000 0.420874598 0.000000e+00 0.00000000
y_pred[13] 0.21820000 0.413065230 0.000000e+00 0.00000000
y_pred[14] 0.22800000 0.419584569 0.000000e+00 0.00000000
y_pred[15] 0.21820000 0.413065230 0.000000e+00 0.00000000
y_pred[16] 0.22960000 0.420617669 0.000000e+00 0.00000000
y_pred[17] 0.22000000 0.414287734 0.000000e+00 0.00000000
y_pred[18] 0.23340000 0.423036916 0.000000e+00 0.00000000
y_pred[19] 0.22560000 0.418018645 0.000000e+00 0.00000000
y_pred[20] 0.21700000 0.412243847 0.000000e+00 0.00000000
y_pred[21] 0.22860000 0.419972994 0.000000e+00 0.00000000
y_pred[22] 0.21860000 0.413337888 0.000000e+00 0.00000000
y_pred[23] 0.22600000 0.418280996 0.000000e+00 0.00000000
y_pred[24] 0.22040000 0.414557851 0.000000e+00 0.00000000
y_pred[25] 0.22720000 0.419064772 0.000000e+00 0.00000000
y_pred[26] 0.22900000 0.420231268 0.000000e+00 0.00000000
y_pred[27] 0.22640000 0.418542800 0.000000e+00 0.00000000
y_pred[28] 0.21940000 0.413881504 0.000000e+00 0.00000000
y_pred[29] 0.22900000 0.420231268 0.000000e+00 0.00000000
y_pred[30] 0.22020000 0.414422863 0.000000e+00 0.00000000
y_pred[31] 0.23100000 0.421514573 0.000000e+00 0.00000000
y_pred[32] 0.21860000 0.413337888 0.000000e+00 0.00000000
y_pred[33] 0.22240000 0.415900030 0.000000e+00 0.00000000
y_pred[34] 0.21640000 0.411831229 0.000000e+00 0.00000000
y_pred[35] 0.22280000 0.416166792 0.000000e+00 0.00000000
y_pred[36] 0.22140000 0.415230687 0.000000e+00 0.00000000
y_pred[37] 0.22840000 0.419843654 0.000000e+00 0.00000000
y_pred[38] 0.23120000 0.421642166 0.000000e+00 0.00000000
y_pred[39] 0.23400000 0.423414520 0.000000e+00 0.00000000
y_pred[40] 0.22180000 0.415498842 0.000000e+00 0.00000000
y_pred[41] 0.22340000 0.416565896 0.000000e+00 0.00000000
y_pred[42] 0.22380000 0.416831272 0.000000e+00 0.00000000
y_pred[43] 0.21980000 0.414152465 0.000000e+00 0.00000000
y_pred[44] 0.22100000 0.414961973 0.000000e+00 0.00000000
y_pred[45] 0.22380000 0.416831272 0.000000e+00 0.00000000
y_pred[46] 0.22500000 0.417624092 0.000000e+00 0.00000000
y_pred[47] 0.22340000 0.416565896 0.000000e+00 0.00000000
y_pred[48] 0.21360000 0.409888572 0.000000e+00 0.00000000
y_pred[49] 0.22100000 0.414961973 0.000000e+00 0.00000000
y_pred[50] 0.22100000 0.414961973 0.000000e+00 0.00000000
y_pred[51] 0.22620000 0.418411967 0.000000e+00 0.00000000
y_pred[52] 0.21920000 0.413745812 0.000000e+00 0.00000000
y_pred[53] 0.21520000 0.411002122 0.000000e+00 0.00000000
y_pred[54] 0.21960000 0.414017055 0.000000e+00 0.00000000
y_pred[55] 0.21720000 0.412381100 0.000000e+00 0.00000000
y_pred[56] 0.22580000 0.418149889 0.000000e+00 0.00000000
y_pred[57] 0.22140000 0.415230687 0.000000e+00 0.00000000
y_pred[58] 0.21240000 0.409047313 0.000000e+00 0.00000000
y_pred[59] 0.23540000 0.424290990 0.000000e+00 0.00000000
y_pred[60] 0.22660000 0.418673497 0.000000e+00 0.00000000
y_pred[61] 0.21340000 0.409748726 0.000000e+00 0.00000000
y_pred[62] 0.22520000 0.417755747 0.000000e+00 0.00000000
y_pred[63] 0.22880000 0.420102198 0.000000e+00 0.00000000
y_pred[64] 0.23000000 0.420874598 0.000000e+00 0.00000000
y_pred[65] 0.22300000 0.416299965 0.000000e+00 0.00000000
y_pred[66] 0.21160000 0.408483551 0.000000e+00 0.00000000
y_pred[67] 0.23340000 0.423036916 0.000000e+00 0.00000000
y_pred[68] 0.21340000 0.409748726 0.000000e+00 0.00000000
y_pred[69] 0.22860000 0.419972994 0.000000e+00 0.00000000
y_pred[70] 0.21880000 0.413474004 0.000000e+00 0.00000000
y_pred[71] 0.21560000 0.411279066 0.000000e+00 0.00000000
y_pred[72] 0.21220000 0.408906592 0.000000e+00 0.00000000
y_pred[73] 0.21960000 0.414017055 0.000000e+00 0.00000000
y_pred[74] 0.22700000 0.418934483 0.000000e+00 0.00000000
y_pred[75] 0.21600000 0.411555434 0.000000e+00 0.00000000
y_pred[76] 0.23640000 0.424913109 0.000000e+00 0.00000000
y_pred[77] 0.22700000 0.418934483 0.000000e+00 0.00000000
y_pred[78] 0.22740000 0.419194925 0.000000e+00 0.00000000
y_pred[79] 0.23020000 0.421002861 0.000000e+00 0.00000000
y_pred[80] 0.22100000 0.414961973 0.000000e+00 0.00000000
y_pred[81] 0.21840000 0.413201630 0.000000e+00 0.00000000
y_pred[82] 0.21940000 0.413881504 0.000000e+00 0.00000000
y_pred[83] 0.21300000 0.409468598 0.000000e+00 0.00000000
y_pred[84] 0.22140000 0.415230687 0.000000e+00 0.00000000
y_pred[85] 0.22000000 0.414287734 0.000000e+00 0.00000000
y_pred[86] 0.22500000 0.417624092 0.000000e+00 0.00000000
y_pred[87] 0.21760000 0.412655179 0.000000e+00 0.00000000
y_pred[88] 0.23240000 0.422404930 0.000000e+00 0.00000000
y_pred[89] 0.22980000 0.420746201 0.000000e+00 0.00000000
y_pred[90] 0.22020000 0.414422863 0.000000e+00 0.00000000
y_pred[91] 0.22080000 0.414827406 0.000000e+00 0.00000000
y_pred[92] 0.22520000 0.417755747 0.000000e+00 0.00000000
y_pred[93] 0.22000000 0.414287734 0.000000e+00 0.00000000
y_pred[94] 0.22920000 0.420360203 0.000000e+00 0.00000000
y_pred[95] 0.22800000 0.419584569 0.000000e+00 0.00000000
y_pred[96] 0.22260000 0.416033480 0.000000e+00 0.00000000
y_pred[97] 0.22680000 0.418804058 0.000000e+00 0.00000000
y_pred[98] 0.22860000 0.419972994 0.000000e+00 0.00000000
y_pred[99] 0.21940000 0.413881504 0.000000e+00 0.00000000
y_pred[100] 0.21980000 0.414152465 0.000000e+00 0.00000000
lp__ -161.05442587 0.966153706 -1.636303e+02 -161.43090870
stats
parameter 50% 75% 97.5%
alpha -3.57609836 -3.44156608 -3.19852989
beta 0.01162678 0.01264862 0.01453086
y_pred[1] 0.00000000 0.00000000 1.00000000
y_pred[2] 0.00000000 0.00000000 1.00000000
y_pred[3] 0.00000000 0.00000000 1.00000000
y_pred[4] 0.00000000 0.00000000 1.00000000
y_pred[5] 0.00000000 0.00000000 1.00000000
y_pred[6] 0.00000000 0.00000000 1.00000000
y_pred[7] 0.00000000 0.00000000 1.00000000
y_pred[8] 0.00000000 0.00000000 1.00000000
y_pred[9] 0.00000000 0.00000000 1.00000000
y_pred[10] 0.00000000 0.00000000 1.00000000
y_pred[11] 0.00000000 0.00000000 1.00000000
y_pred[12] 0.00000000 0.00000000 1.00000000
y_pred[13] 0.00000000 0.00000000 1.00000000
y_pred[14] 0.00000000 0.00000000 1.00000000
y_pred[15] 0.00000000 0.00000000 1.00000000
y_pred[16] 0.00000000 0.00000000 1.00000000
y_pred[17] 0.00000000 0.00000000 1.00000000
y_pred[18] 0.00000000 0.00000000 1.00000000
y_pred[19] 0.00000000 0.00000000 1.00000000
y_pred[20] 0.00000000 0.00000000 1.00000000
y_pred[21] 0.00000000 0.00000000 1.00000000
y_pred[22] 0.00000000 0.00000000 1.00000000
y_pred[23] 0.00000000 0.00000000 1.00000000
y_pred[24] 0.00000000 0.00000000 1.00000000
y_pred[25] 0.00000000 0.00000000 1.00000000
y_pred[26] 0.00000000 0.00000000 1.00000000
y_pred[27] 0.00000000 0.00000000 1.00000000
y_pred[28] 0.00000000 0.00000000 1.00000000
y_pred[29] 0.00000000 0.00000000 1.00000000
y_pred[30] 0.00000000 0.00000000 1.00000000
y_pred[31] 0.00000000 0.00000000 1.00000000
y_pred[32] 0.00000000 0.00000000 1.00000000
y_pred[33] 0.00000000 0.00000000 1.00000000
y_pred[34] 0.00000000 0.00000000 1.00000000
y_pred[35] 0.00000000 0.00000000 1.00000000
y_pred[36] 0.00000000 0.00000000 1.00000000
y_pred[37] 0.00000000 0.00000000 1.00000000
y_pred[38] 0.00000000 0.00000000 1.00000000
y_pred[39] 0.00000000 0.00000000 1.00000000
y_pred[40] 0.00000000 0.00000000 1.00000000
y_pred[41] 0.00000000 0.00000000 1.00000000
y_pred[42] 0.00000000 0.00000000 1.00000000
y_pred[43] 0.00000000 0.00000000 1.00000000
y_pred[44] 0.00000000 0.00000000 1.00000000
y_pred[45] 0.00000000 0.00000000 1.00000000
y_pred[46] 0.00000000 0.00000000 1.00000000
y_pred[47] 0.00000000 0.00000000 1.00000000
y_pred[48] 0.00000000 0.00000000 1.00000000
y_pred[49] 0.00000000 0.00000000 1.00000000
y_pred[50] 0.00000000 0.00000000 1.00000000
y_pred[51] 0.00000000 0.00000000 1.00000000
y_pred[52] 0.00000000 0.00000000 1.00000000
y_pred[53] 0.00000000 0.00000000 1.00000000
y_pred[54] 0.00000000 0.00000000 1.00000000
y_pred[55] 0.00000000 0.00000000 1.00000000
y_pred[56] 0.00000000 0.00000000 1.00000000
y_pred[57] 0.00000000 0.00000000 1.00000000
y_pred[58] 0.00000000 0.00000000 1.00000000
y_pred[59] 0.00000000 0.00000000 1.00000000
y_pred[60] 0.00000000 0.00000000 1.00000000
y_pred[61] 0.00000000 0.00000000 1.00000000
y_pred[62] 0.00000000 0.00000000 1.00000000
y_pred[63] 0.00000000 0.00000000 1.00000000
y_pred[64] 0.00000000 0.00000000 1.00000000
y_pred[65] 0.00000000 0.00000000 1.00000000
y_pred[66] 0.00000000 0.00000000 1.00000000
y_pred[67] 0.00000000 0.00000000 1.00000000
y_pred[68] 0.00000000 0.00000000 1.00000000
y_pred[69] 0.00000000 0.00000000 1.00000000
y_pred[70] 0.00000000 0.00000000 1.00000000
y_pred[71] 0.00000000 0.00000000 1.00000000
y_pred[72] 0.00000000 0.00000000 1.00000000
y_pred[73] 0.00000000 0.00000000 1.00000000
y_pred[74] 0.00000000 0.00000000 1.00000000
y_pred[75] 0.00000000 0.00000000 1.00000000
y_pred[76] 0.00000000 0.00000000 1.00000000
y_pred[77] 0.00000000 0.00000000 1.00000000
y_pred[78] 0.00000000 0.00000000 1.00000000
y_pred[79] 0.00000000 0.00000000 1.00000000
y_pred[80] 0.00000000 0.00000000 1.00000000
y_pred[81] 0.00000000 0.00000000 1.00000000
y_pred[82] 0.00000000 0.00000000 1.00000000
y_pred[83] 0.00000000 0.00000000 1.00000000
y_pred[84] 0.00000000 0.00000000 1.00000000
y_pred[85] 0.00000000 0.00000000 1.00000000
y_pred[86] 0.00000000 0.00000000 1.00000000
y_pred[87] 0.00000000 0.00000000 1.00000000
y_pred[88] 0.00000000 0.00000000 1.00000000
y_pred[89] 0.00000000 0.00000000 1.00000000
y_pred[90] 0.00000000 0.00000000 1.00000000
y_pred[91] 0.00000000 0.00000000 1.00000000
y_pred[92] 0.00000000 0.00000000 1.00000000
y_pred[93] 0.00000000 0.00000000 1.00000000
y_pred[94] 0.00000000 0.00000000 1.00000000
y_pred[95] 0.00000000 0.00000000 1.00000000
y_pred[96] 0.00000000 0.00000000 1.00000000
y_pred[97] 0.00000000 0.00000000 1.00000000
y_pred[98] 0.00000000 0.00000000 1.00000000
y_pred[99] 0.00000000 0.00000000 1.00000000
y_pred[100] 0.00000000 0.00000000 1.00000000
lp__ -160.74720082 -160.36856097 -160.11043142
, , chains = chain:2
stats
parameter mean sd 2.5% 25%
alpha -3.58009001 0.211420338 -4.003340e+00 -3.72166999
beta 0.01159313 0.001483096 8.694391e-03 0.01057645
y_pred[1] 0.21980000 0.414152465 0.000000e+00 0.00000000
y_pred[2] 0.22400000 0.416963754 0.000000e+00 0.00000000
y_pred[3] 0.22500000 0.417624092 0.000000e+00 0.00000000
y_pred[4] 0.23080000 0.421386845 0.000000e+00 0.00000000
y_pred[5] 0.21840000 0.413201630 0.000000e+00 0.00000000
y_pred[6] 0.22460000 0.417360369 0.000000e+00 0.00000000
y_pred[7] 0.22160000 0.415364834 0.000000e+00 0.00000000
y_pred[8] 0.21920000 0.413745812 0.000000e+00 0.00000000
y_pred[9] 0.22620000 0.418411967 0.000000e+00 0.00000000
y_pred[10] 0.22620000 0.418411967 0.000000e+00 0.00000000
y_pred[11] 0.22080000 0.414827406 0.000000e+00 0.00000000
y_pred[12] 0.23000000 0.420874598 0.000000e+00 0.00000000
y_pred[13] 0.22240000 0.415900030 0.000000e+00 0.00000000
y_pred[14] 0.22420000 0.417096097 0.000000e+00 0.00000000
y_pred[15] 0.22440000 0.417228302 0.000000e+00 0.00000000
y_pred[16] 0.22900000 0.420231268 0.000000e+00 0.00000000
y_pred[17] 0.22960000 0.420617669 0.000000e+00 0.00000000
y_pred[18] 0.22220000 0.415766440 0.000000e+00 0.00000000
y_pred[19] 0.20900000 0.406635058 0.000000e+00 0.00000000
y_pred[20] 0.22720000 0.419064772 0.000000e+00 0.00000000
y_pred[21] 0.22020000 0.414422863 0.000000e+00 0.00000000
y_pred[22] 0.22500000 0.417624092 0.000000e+00 0.00000000
y_pred[23] 0.22720000 0.419064772 0.000000e+00 0.00000000
y_pred[24] 0.22400000 0.416963754 0.000000e+00 0.00000000
y_pred[25] 0.22100000 0.414961973 0.000000e+00 0.00000000
y_pred[26] 0.22100000 0.414961973 0.000000e+00 0.00000000
y_pred[27] 0.21540000 0.411140666 0.000000e+00 0.00000000
y_pred[28] 0.22520000 0.417755747 0.000000e+00 0.00000000
y_pred[29] 0.22160000 0.415364834 0.000000e+00 0.00000000
y_pred[30] 0.22000000 0.414287734 0.000000e+00 0.00000000
y_pred[31] 0.21440000 0.410446505 0.000000e+00 0.00000000
y_pred[32] 0.23680000 0.425161043 0.000000e+00 0.00000000
y_pred[33] 0.22720000 0.419064772 0.000000e+00 0.00000000
y_pred[34] 0.21520000 0.411002122 0.000000e+00 0.00000000
y_pred[35] 0.22400000 0.416963754 0.000000e+00 0.00000000
y_pred[36] 0.22320000 0.416433000 0.000000e+00 0.00000000
y_pred[37] 0.23060000 0.421258984 0.000000e+00 0.00000000
y_pred[38] 0.22500000 0.417624092 0.000000e+00 0.00000000
y_pred[39] 0.23140000 0.421769627 0.000000e+00 0.00000000
y_pred[40] 0.22680000 0.418804058 0.000000e+00 0.00000000
y_pred[41] 0.22540000 0.417887265 0.000000e+00 0.00000000
y_pred[42] 0.21700000 0.412243847 0.000000e+00 0.00000000
y_pred[43] 0.22340000 0.416565896 0.000000e+00 0.00000000
y_pred[44] 0.21820000 0.413065230 0.000000e+00 0.00000000
y_pred[45] 0.22600000 0.418280996 0.000000e+00 0.00000000
y_pred[46] 0.22560000 0.418018645 0.000000e+00 0.00000000
y_pred[47] 0.23040000 0.421130989 0.000000e+00 0.00000000
y_pred[48] 0.22400000 0.416963754 0.000000e+00 0.00000000
y_pred[49] 0.21980000 0.414152465 0.000000e+00 0.00000000
y_pred[50] 0.22320000 0.416433000 0.000000e+00 0.00000000
y_pred[51] 0.22340000 0.416565896 0.000000e+00 0.00000000
y_pred[52] 0.22500000 0.417624092 0.000000e+00 0.00000000
y_pred[53] 0.21900000 0.413609979 0.000000e+00 0.00000000
y_pred[54] 0.23160000 0.421896954 0.000000e+00 0.00000000
y_pred[55] 0.22160000 0.415364834 0.000000e+00 0.00000000
y_pred[56] 0.21480000 0.410724602 0.000000e+00 0.00000000
y_pred[57] 0.21940000 0.413881504 0.000000e+00 0.00000000
y_pred[58] 0.22120000 0.415096400 0.000000e+00 0.00000000
y_pred[59] 0.23020000 0.421002861 0.000000e+00 0.00000000
y_pred[60] 0.22160000 0.415364834 0.000000e+00 0.00000000
y_pred[61] 0.23180000 0.422024147 0.000000e+00 0.00000000
y_pred[62] 0.22860000 0.419972994 0.000000e+00 0.00000000
y_pred[63] 0.22140000 0.415230687 0.000000e+00 0.00000000
y_pred[64] 0.21720000 0.412381100 0.000000e+00 0.00000000
y_pred[65] 0.22480000 0.417492299 0.000000e+00 0.00000000
y_pred[66] 0.22420000 0.417096097 0.000000e+00 0.00000000
y_pred[67] 0.21940000 0.413881504 0.000000e+00 0.00000000
y_pred[68] 0.22260000 0.416033480 0.000000e+00 0.00000000
y_pred[69] 0.22800000 0.419584569 0.000000e+00 0.00000000
y_pred[70] 0.21960000 0.414017055 0.000000e+00 0.00000000
y_pred[71] 0.21340000 0.409748726 0.000000e+00 0.00000000
y_pred[72] 0.21420000 0.410307239 0.000000e+00 0.00000000
y_pred[73] 0.22320000 0.416433000 0.000000e+00 0.00000000
y_pred[74] 0.21500000 0.410863434 0.000000e+00 0.00000000
y_pred[75] 0.22000000 0.414287734 0.000000e+00 0.00000000
y_pred[76] 0.22920000 0.420360203 0.000000e+00 0.00000000
y_pred[77] 0.21700000 0.412243847 0.000000e+00 0.00000000
y_pred[78] 0.22220000 0.415766440 0.000000e+00 0.00000000
y_pred[79] 0.23240000 0.422404930 0.000000e+00 0.00000000
y_pred[80] 0.22120000 0.415096400 0.000000e+00 0.00000000
y_pred[81] 0.21760000 0.412655179 0.000000e+00 0.00000000
y_pred[82] 0.23400000 0.423414520 0.000000e+00 0.00000000
y_pred[83] 0.22320000 0.416433000 0.000000e+00 0.00000000
y_pred[84] 0.22520000 0.417755747 0.000000e+00 0.00000000
y_pred[85] 0.22180000 0.415498842 0.000000e+00 0.00000000
y_pred[86] 0.22360000 0.416698653 0.000000e+00 0.00000000
y_pred[87] 0.23380000 0.423288784 0.000000e+00 0.00000000
y_pred[88] 0.22260000 0.416033480 0.000000e+00 0.00000000
y_pred[89] 0.21300000 0.409468598 0.000000e+00 0.00000000
y_pred[90] 0.22280000 0.416166792 0.000000e+00 0.00000000
y_pred[91] 0.22820000 0.419714179 0.000000e+00 0.00000000
y_pred[92] 0.21940000 0.413881504 0.000000e+00 0.00000000
y_pred[93] 0.23400000 0.423414520 0.000000e+00 0.00000000
y_pred[94] 0.22420000 0.417096097 0.000000e+00 0.00000000
y_pred[95] 0.22580000 0.418149889 0.000000e+00 0.00000000
y_pred[96] 0.22720000 0.419064772 0.000000e+00 0.00000000
y_pred[97] 0.21800000 0.412928689 0.000000e+00 0.00000000
y_pred[98] 0.22680000 0.418804058 0.000000e+00 0.00000000
y_pred[99] 0.23380000 0.423288784 0.000000e+00 0.00000000
y_pred[100] 0.21800000 0.412928689 0.000000e+00 0.00000000
lp__ -161.07385294 0.969693235 -1.636585e+02 -161.43673140
stats
parameter 50% 75% 97.5%
alpha -3.57815609 -3.43200331 -3.16650609
beta 0.01160543 0.01260413 0.01454586
y_pred[1] 0.00000000 0.00000000 1.00000000
y_pred[2] 0.00000000 0.00000000 1.00000000
y_pred[3] 0.00000000 0.00000000 1.00000000
y_pred[4] 0.00000000 0.00000000 1.00000000
y_pred[5] 0.00000000 0.00000000 1.00000000
y_pred[6] 0.00000000 0.00000000 1.00000000
y_pred[7] 0.00000000 0.00000000 1.00000000
y_pred[8] 0.00000000 0.00000000 1.00000000
y_pred[9] 0.00000000 0.00000000 1.00000000
y_pred[10] 0.00000000 0.00000000 1.00000000
y_pred[11] 0.00000000 0.00000000 1.00000000
y_pred[12] 0.00000000 0.00000000 1.00000000
y_pred[13] 0.00000000 0.00000000 1.00000000
y_pred[14] 0.00000000 0.00000000 1.00000000
y_pred[15] 0.00000000 0.00000000 1.00000000
y_pred[16] 0.00000000 0.00000000 1.00000000
y_pred[17] 0.00000000 0.00000000 1.00000000
y_pred[18] 0.00000000 0.00000000 1.00000000
y_pred[19] 0.00000000 0.00000000 1.00000000
y_pred[20] 0.00000000 0.00000000 1.00000000
y_pred[21] 0.00000000 0.00000000 1.00000000
y_pred[22] 0.00000000 0.00000000 1.00000000
y_pred[23] 0.00000000 0.00000000 1.00000000
y_pred[24] 0.00000000 0.00000000 1.00000000
y_pred[25] 0.00000000 0.00000000 1.00000000
y_pred[26] 0.00000000 0.00000000 1.00000000
y_pred[27] 0.00000000 0.00000000 1.00000000
y_pred[28] 0.00000000 0.00000000 1.00000000
y_pred[29] 0.00000000 0.00000000 1.00000000
y_pred[30] 0.00000000 0.00000000 1.00000000
y_pred[31] 0.00000000 0.00000000 1.00000000
y_pred[32] 0.00000000 0.00000000 1.00000000
y_pred[33] 0.00000000 0.00000000 1.00000000
y_pred[34] 0.00000000 0.00000000 1.00000000
y_pred[35] 0.00000000 0.00000000 1.00000000
y_pred[36] 0.00000000 0.00000000 1.00000000
y_pred[37] 0.00000000 0.00000000 1.00000000
y_pred[38] 0.00000000 0.00000000 1.00000000
y_pred[39] 0.00000000 0.00000000 1.00000000
y_pred[40] 0.00000000 0.00000000 1.00000000
y_pred[41] 0.00000000 0.00000000 1.00000000
y_pred[42] 0.00000000 0.00000000 1.00000000
y_pred[43] 0.00000000 0.00000000 1.00000000
y_pred[44] 0.00000000 0.00000000 1.00000000
y_pred[45] 0.00000000 0.00000000 1.00000000
y_pred[46] 0.00000000 0.00000000 1.00000000
y_pred[47] 0.00000000 0.00000000 1.00000000
y_pred[48] 0.00000000 0.00000000 1.00000000
y_pred[49] 0.00000000 0.00000000 1.00000000
y_pred[50] 0.00000000 0.00000000 1.00000000
y_pred[51] 0.00000000 0.00000000 1.00000000
y_pred[52] 0.00000000 0.00000000 1.00000000
y_pred[53] 0.00000000 0.00000000 1.00000000
y_pred[54] 0.00000000 0.00000000 1.00000000
y_pred[55] 0.00000000 0.00000000 1.00000000
y_pred[56] 0.00000000 0.00000000 1.00000000
y_pred[57] 0.00000000 0.00000000 1.00000000
y_pred[58] 0.00000000 0.00000000 1.00000000
y_pred[59] 0.00000000 0.00000000 1.00000000
y_pred[60] 0.00000000 0.00000000 1.00000000
y_pred[61] 0.00000000 0.00000000 1.00000000
y_pred[62] 0.00000000 0.00000000 1.00000000
y_pred[63] 0.00000000 0.00000000 1.00000000
y_pred[64] 0.00000000 0.00000000 1.00000000
y_pred[65] 0.00000000 0.00000000 1.00000000
y_pred[66] 0.00000000 0.00000000 1.00000000
y_pred[67] 0.00000000 0.00000000 1.00000000
y_pred[68] 0.00000000 0.00000000 1.00000000
y_pred[69] 0.00000000 0.00000000 1.00000000
y_pred[70] 0.00000000 0.00000000 1.00000000
y_pred[71] 0.00000000 0.00000000 1.00000000
y_pred[72] 0.00000000 0.00000000 1.00000000
y_pred[73] 0.00000000 0.00000000 1.00000000
y_pred[74] 0.00000000 0.00000000 1.00000000
y_pred[75] 0.00000000 0.00000000 1.00000000
y_pred[76] 0.00000000 0.00000000 1.00000000
y_pred[77] 0.00000000 0.00000000 1.00000000
y_pred[78] 0.00000000 0.00000000 1.00000000
y_pred[79] 0.00000000 0.00000000 1.00000000
y_pred[80] 0.00000000 0.00000000 1.00000000
y_pred[81] 0.00000000 0.00000000 1.00000000
y_pred[82] 0.00000000 0.00000000 1.00000000
y_pred[83] 0.00000000 0.00000000 1.00000000
y_pred[84] 0.00000000 0.00000000 1.00000000
y_pred[85] 0.00000000 0.00000000 1.00000000
y_pred[86] 0.00000000 0.00000000 1.00000000
y_pred[87] 0.00000000 0.00000000 1.00000000
y_pred[88] 0.00000000 0.00000000 1.00000000
y_pred[89] 0.00000000 0.00000000 1.00000000
y_pred[90] 0.00000000 0.00000000 1.00000000
y_pred[91] 0.00000000 0.00000000 1.00000000
y_pred[92] 0.00000000 0.00000000 1.00000000
y_pred[93] 0.00000000 0.00000000 1.00000000
y_pred[94] 0.00000000 0.00000000 1.00000000
y_pred[95] 0.00000000 0.00000000 1.00000000
y_pred[96] 0.00000000 0.00000000 1.00000000
y_pred[97] 0.00000000 0.00000000 1.00000000
y_pred[98] 0.00000000 0.00000000 1.00000000
y_pred[99] 0.00000000 0.00000000 1.00000000
y_pred[100] 0.00000000 0.00000000 1.00000000
lp__ -160.78427235 -160.38381362 -160.11240738
, , chains = chain:3
stats
parameter mean sd 2.5% 25% 50%
alpha -3.59626185 0.211435362 -4.031046e+00 -3.7349649 -3.590462
beta 0.01170564 0.001484847 8.830389e-03 0.0106871 0.011687
y_pred[1] 0.23620000 0.424788947 0.000000e+00 0.0000000 0.000000
y_pred[2] 0.21840000 0.413201630 0.000000e+00 0.0000000 0.000000
y_pred[3] 0.21840000 0.413201630 0.000000e+00 0.0000000 0.000000
y_pred[4] 0.22500000 0.417624092 0.000000e+00 0.0000000 0.000000
y_pred[5] 0.22940000 0.420489004 0.000000e+00 0.0000000 0.000000
y_pred[6] 0.21200000 0.408765725 0.000000e+00 0.0000000 0.000000
y_pred[7] 0.23140000 0.421769627 0.000000e+00 0.0000000 0.000000
y_pred[8] 0.23000000 0.420874598 0.000000e+00 0.0000000 0.000000
y_pred[9] 0.23580000 0.424540230 0.000000e+00 0.0000000 0.000000
y_pred[10] 0.21800000 0.412928689 0.000000e+00 0.0000000 0.000000
y_pred[11] 0.21980000 0.414152465 0.000000e+00 0.0000000 0.000000
y_pred[12] 0.22180000 0.415498842 0.000000e+00 0.0000000 0.000000
y_pred[13] 0.22060000 0.414692698 0.000000e+00 0.0000000 0.000000
y_pred[14] 0.21840000 0.413201630 0.000000e+00 0.0000000 0.000000
y_pred[15] 0.21240000 0.409047313 0.000000e+00 0.0000000 0.000000
y_pred[16] 0.21620000 0.411693403 0.000000e+00 0.0000000 0.000000
y_pred[17] 0.22200000 0.415632711 0.000000e+00 0.0000000 0.000000
y_pred[18] 0.22840000 0.419843654 0.000000e+00 0.0000000 0.000000
y_pred[19] 0.22920000 0.420360203 0.000000e+00 0.0000000 0.000000
y_pred[20] 0.22280000 0.416166792 0.000000e+00 0.0000000 0.000000
y_pred[21] 0.22580000 0.418149889 0.000000e+00 0.0000000 0.000000
y_pred[22] 0.22560000 0.418018645 0.000000e+00 0.0000000 0.000000
y_pred[23] 0.22280000 0.416166792 0.000000e+00 0.0000000 0.000000
y_pred[24] 0.21840000 0.413201630 0.000000e+00 0.0000000 0.000000
y_pred[25] 0.22320000 0.416433000 0.000000e+00 0.0000000 0.000000
y_pred[26] 0.22460000 0.417360369 0.000000e+00 0.0000000 0.000000
y_pred[27] 0.21880000 0.413474004 0.000000e+00 0.0000000 0.000000
y_pred[28] 0.22620000 0.418411967 0.000000e+00 0.0000000 0.000000
y_pred[29] 0.22680000 0.418804058 0.000000e+00 0.0000000 0.000000
y_pred[30] 0.22100000 0.414961973 0.000000e+00 0.0000000 0.000000
y_pred[31] 0.21880000 0.413474004 0.000000e+00 0.0000000 0.000000
y_pred[32] 0.23000000 0.420874598 0.000000e+00 0.0000000 0.000000
y_pred[33] 0.22880000 0.420102198 0.000000e+00 0.0000000 0.000000
y_pred[34] 0.22160000 0.415364834 0.000000e+00 0.0000000 0.000000
y_pred[35] 0.21420000 0.410307239 0.000000e+00 0.0000000 0.000000
y_pred[36] 0.21940000 0.413881504 0.000000e+00 0.0000000 0.000000
y_pred[37] 0.22020000 0.414422863 0.000000e+00 0.0000000 0.000000
y_pred[38] 0.20940000 0.406921070 0.000000e+00 0.0000000 0.000000
y_pred[39] 0.21980000 0.414152465 0.000000e+00 0.0000000 0.000000
y_pred[40] 0.21080000 0.407917442 0.000000e+00 0.0000000 0.000000
y_pred[41] 0.22100000 0.414961973 0.000000e+00 0.0000000 0.000000
y_pred[42] 0.22220000 0.415766440 0.000000e+00 0.0000000 0.000000
y_pred[43] 0.23380000 0.423288784 0.000000e+00 0.0000000 0.000000
y_pred[44] 0.23420000 0.423540125 0.000000e+00 0.0000000 0.000000
y_pred[45] 0.22460000 0.417360369 0.000000e+00 0.0000000 0.000000
y_pred[46] 0.22280000 0.416166792 0.000000e+00 0.0000000 0.000000
y_pred[47] 0.22500000 0.417624092 0.000000e+00 0.0000000 0.000000
y_pred[48] 0.21500000 0.410863434 0.000000e+00 0.0000000 0.000000
y_pred[49] 0.23060000 0.421258984 0.000000e+00 0.0000000 0.000000
y_pred[50] 0.24000000 0.427125845 0.000000e+00 0.0000000 0.000000
y_pred[51] 0.21780000 0.412792005 0.000000e+00 0.0000000 0.000000
y_pred[52] 0.21540000 0.411140666 0.000000e+00 0.0000000 0.000000
y_pred[53] 0.23040000 0.421130989 0.000000e+00 0.0000000 0.000000
y_pred[54] 0.23200000 0.422151208 0.000000e+00 0.0000000 0.000000
y_pred[55] 0.21820000 0.413065230 0.000000e+00 0.0000000 0.000000
y_pred[56] 0.22200000 0.415632711 0.000000e+00 0.0000000 0.000000
y_pred[57] 0.21580000 0.411417322 0.000000e+00 0.0000000 0.000000
y_pred[58] 0.21680000 0.412106450 0.000000e+00 0.0000000 0.000000
y_pred[59] 0.23640000 0.424913109 0.000000e+00 0.0000000 0.000000
y_pred[60] 0.23360000 0.423162916 0.000000e+00 0.0000000 0.000000
y_pred[61] 0.22660000 0.418673497 0.000000e+00 0.0000000 0.000000
y_pred[62] 0.22420000 0.417096097 0.000000e+00 0.0000000 0.000000
y_pred[63] 0.21340000 0.409748726 0.000000e+00 0.0000000 0.000000
y_pred[64] 0.22400000 0.416963754 0.000000e+00 0.0000000 0.000000
y_pred[65] 0.21660000 0.411968911 0.000000e+00 0.0000000 0.000000
y_pred[66] 0.22700000 0.418934483 0.000000e+00 0.0000000 0.000000
y_pred[67] 0.23280000 0.422658122 0.000000e+00 0.0000000 0.000000
y_pred[68] 0.21660000 0.411968911 0.000000e+00 0.0000000 0.000000
y_pred[69] 0.22060000 0.414692698 0.000000e+00 0.0000000 0.000000
y_pred[70] 0.22320000 0.416433000 0.000000e+00 0.0000000 0.000000
y_pred[71] 0.22380000 0.416831272 0.000000e+00 0.0000000 0.000000
y_pred[72] 0.23140000 0.421769627 0.000000e+00 0.0000000 0.000000
y_pred[73] 0.22160000 0.415364834 0.000000e+00 0.0000000 0.000000
y_pred[74] 0.21000000 0.407348974 0.000000e+00 0.0000000 0.000000
y_pred[75] 0.21800000 0.412928689 0.000000e+00 0.0000000 0.000000
y_pred[76] 0.21780000 0.412792005 0.000000e+00 0.0000000 0.000000
y_pred[77] 0.23400000 0.423414520 0.000000e+00 0.0000000 0.000000
y_pred[78] 0.22580000 0.418149889 0.000000e+00 0.0000000 0.000000
y_pred[79] 0.23360000 0.423162916 0.000000e+00 0.0000000 0.000000
y_pred[80] 0.21800000 0.412928689 0.000000e+00 0.0000000 0.000000
y_pred[81] 0.22100000 0.414961973 0.000000e+00 0.0000000 0.000000
y_pred[82] 0.22580000 0.418149889 0.000000e+00 0.0000000 0.000000
y_pred[83] 0.22480000 0.417492299 0.000000e+00 0.0000000 0.000000
y_pred[84] 0.22320000 0.416433000 0.000000e+00 0.0000000 0.000000
y_pred[85] 0.22900000 0.420231268 0.000000e+00 0.0000000 0.000000
y_pred[86] 0.23080000 0.421386845 0.000000e+00 0.0000000 0.000000
y_pred[87] 0.22100000 0.414961973 0.000000e+00 0.0000000 0.000000
y_pred[88] 0.22980000 0.420746201 0.000000e+00 0.0000000 0.000000
y_pred[89] 0.23840000 0.426147580 0.000000e+00 0.0000000 0.000000
y_pred[90] 0.22860000 0.419972994 0.000000e+00 0.0000000 0.000000
y_pred[91] 0.23060000 0.421258984 0.000000e+00 0.0000000 0.000000
y_pred[92] 0.22460000 0.417360369 0.000000e+00 0.0000000 0.000000
y_pred[93] 0.23000000 0.420874598 0.000000e+00 0.0000000 0.000000
y_pred[94] 0.22080000 0.414827406 0.000000e+00 0.0000000 0.000000
y_pred[95] 0.23140000 0.421769627 0.000000e+00 0.0000000 0.000000
y_pred[96] 0.23720000 0.425408456 0.000000e+00 0.0000000 0.000000
y_pred[97] 0.22740000 0.419194925 0.000000e+00 0.0000000 0.000000
y_pred[98] 0.23040000 0.421130989 0.000000e+00 0.0000000 0.000000
y_pred[99] 0.21380000 0.410028273 0.000000e+00 0.0000000 0.000000
y_pred[100] 0.22760000 0.419324942 0.000000e+00 0.0000000 0.000000
lp__ -161.08888887 0.998675899 -1.636752e+02 -161.4835253 -160.784328
stats
parameter 75% 97.5%
alpha -3.44846283 -3.20776066
beta 0.01273215 0.01464098
y_pred[1] 0.00000000 1.00000000
y_pred[2] 0.00000000 1.00000000
y_pred[3] 0.00000000 1.00000000
y_pred[4] 0.00000000 1.00000000
y_pred[5] 0.00000000 1.00000000
y_pred[6] 0.00000000 1.00000000
y_pred[7] 0.00000000 1.00000000
y_pred[8] 0.00000000 1.00000000
y_pred[9] 0.00000000 1.00000000
y_pred[10] 0.00000000 1.00000000
y_pred[11] 0.00000000 1.00000000
y_pred[12] 0.00000000 1.00000000
y_pred[13] 0.00000000 1.00000000
y_pred[14] 0.00000000 1.00000000
y_pred[15] 0.00000000 1.00000000
y_pred[16] 0.00000000 1.00000000
y_pred[17] 0.00000000 1.00000000
y_pred[18] 0.00000000 1.00000000
y_pred[19] 0.00000000 1.00000000
y_pred[20] 0.00000000 1.00000000
y_pred[21] 0.00000000 1.00000000
y_pred[22] 0.00000000 1.00000000
y_pred[23] 0.00000000 1.00000000
y_pred[24] 0.00000000 1.00000000
y_pred[25] 0.00000000 1.00000000
y_pred[26] 0.00000000 1.00000000
y_pred[27] 0.00000000 1.00000000
y_pred[28] 0.00000000 1.00000000
y_pred[29] 0.00000000 1.00000000
y_pred[30] 0.00000000 1.00000000
y_pred[31] 0.00000000 1.00000000
y_pred[32] 0.00000000 1.00000000
y_pred[33] 0.00000000 1.00000000
y_pred[34] 0.00000000 1.00000000
y_pred[35] 0.00000000 1.00000000
y_pred[36] 0.00000000 1.00000000
y_pred[37] 0.00000000 1.00000000
y_pred[38] 0.00000000 1.00000000
y_pred[39] 0.00000000 1.00000000
y_pred[40] 0.00000000 1.00000000
y_pred[41] 0.00000000 1.00000000
y_pred[42] 0.00000000 1.00000000
y_pred[43] 0.00000000 1.00000000
y_pred[44] 0.00000000 1.00000000
y_pred[45] 0.00000000 1.00000000
y_pred[46] 0.00000000 1.00000000
y_pred[47] 0.00000000 1.00000000
y_pred[48] 0.00000000 1.00000000
y_pred[49] 0.00000000 1.00000000
y_pred[50] 0.00000000 1.00000000
y_pred[51] 0.00000000 1.00000000
y_pred[52] 0.00000000 1.00000000
y_pred[53] 0.00000000 1.00000000
y_pred[54] 0.00000000 1.00000000
y_pred[55] 0.00000000 1.00000000
y_pred[56] 0.00000000 1.00000000
y_pred[57] 0.00000000 1.00000000
y_pred[58] 0.00000000 1.00000000
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y_pred[60] 0.00000000 1.00000000
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y_pred[69] 0.00000000 1.00000000
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y_pred[75] 0.00000000 1.00000000
y_pred[76] 0.00000000 1.00000000
y_pred[77] 0.00000000 1.00000000
y_pred[78] 0.00000000 1.00000000
y_pred[79] 0.00000000 1.00000000
y_pred[80] 0.00000000 1.00000000
y_pred[81] 0.00000000 1.00000000
y_pred[82] 0.00000000 1.00000000
y_pred[83] 0.00000000 1.00000000
y_pred[84] 0.00000000 1.00000000
y_pred[85] 0.00000000 1.00000000
y_pred[86] 0.00000000 1.00000000
y_pred[87] 0.00000000 1.00000000
y_pred[88] 0.00000000 1.00000000
y_pred[89] 0.00000000 1.00000000
y_pred[90] 0.00000000 1.00000000
y_pred[91] 0.00000000 1.00000000
y_pred[92] 0.00000000 1.00000000
y_pred[93] 0.00000000 1.00000000
y_pred[94] 0.00000000 1.00000000
y_pred[95] 0.00000000 1.00000000
y_pred[96] 0.00000000 1.00000000
y_pred[97] 0.00000000 1.00000000
y_pred[98] 0.00000000 1.00000000
y_pred[99] 0.00000000 1.00000000
y_pred[100] 0.00000000 1.00000000
lp__ -160.37876368 -160.11232189
, , chains = chain:4
stats
parameter mean sd 2.5% 25%
alpha -3.58524741 0.214041455 -4.014947e+00 -3.72714404
beta 0.01162728 0.001481988 8.699375e-03 0.01066153
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y_pred[2] 0.23320000 0.422910783 0.000000e+00 0.00000000
y_pred[3] 0.21960000 0.414017055 0.000000e+00 0.00000000
y_pred[4] 0.20700000 0.405196047 0.000000e+00 0.00000000
y_pred[5] 0.21700000 0.412243847 0.000000e+00 0.00000000
y_pred[6] 0.22220000 0.415766440 0.000000e+00 0.00000000
y_pred[7] 0.22460000 0.417360369 0.000000e+00 0.00000000
y_pred[8] 0.21380000 0.410028273 0.000000e+00 0.00000000
y_pred[9] 0.23280000 0.422658122 0.000000e+00 0.00000000
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y_pred[40] 0.23100000 0.421514573 0.000000e+00 0.00000000
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y_pred[71] 0.21980000 0.414152465 0.000000e+00 0.00000000
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y_pred[73] 0.22340000 0.416565896 0.000000e+00 0.00000000
y_pred[74] 0.22000000 0.414287734 0.000000e+00 0.00000000
y_pred[75] 0.22160000 0.415364834 0.000000e+00 0.00000000
y_pred[76] 0.22740000 0.419194925 0.000000e+00 0.00000000
y_pred[77] 0.21540000 0.411140666 0.000000e+00 0.00000000
y_pred[78] 0.21580000 0.411417322 0.000000e+00 0.00000000
y_pred[79] 0.21560000 0.411279066 0.000000e+00 0.00000000
y_pred[80] 0.22080000 0.414827406 0.000000e+00 0.00000000
y_pred[81] 0.22220000 0.415766440 0.000000e+00 0.00000000
y_pred[82] 0.22020000 0.414422863 0.000000e+00 0.00000000
y_pred[83] 0.21780000 0.412792005 0.000000e+00 0.00000000
y_pred[84] 0.23520000 0.424166174 0.000000e+00 0.00000000
y_pred[85] 0.22000000 0.414287734 0.000000e+00 0.00000000
y_pred[86] 0.23200000 0.422151208 0.000000e+00 0.00000000
y_pred[87] 0.23300000 0.422784519 0.000000e+00 0.00000000
y_pred[88] 0.21980000 0.414152465 0.000000e+00 0.00000000
y_pred[89] 0.22520000 0.417755747 0.000000e+00 0.00000000
y_pred[90] 0.22640000 0.418542800 0.000000e+00 0.00000000
y_pred[91] 0.22120000 0.415096400 0.000000e+00 0.00000000
y_pred[92] 0.21240000 0.409047313 0.000000e+00 0.00000000
y_pred[93] 0.23240000 0.422404930 0.000000e+00 0.00000000
y_pred[94] 0.21620000 0.411693403 0.000000e+00 0.00000000
y_pred[95] 0.21820000 0.413065230 0.000000e+00 0.00000000
y_pred[96] 0.22180000 0.415498842 0.000000e+00 0.00000000
y_pred[97] 0.21780000 0.412792005 0.000000e+00 0.00000000
y_pred[98] 0.21820000 0.413065230 0.000000e+00 0.00000000
y_pred[99] 0.21920000 0.413745812 0.000000e+00 0.00000000
y_pred[100] 0.23340000 0.423036916 0.000000e+00 0.00000000
lp__ -161.08578738 0.989778257 -1.637699e+02 -161.47302928
stats
parameter 50% 75% 97.5%
alpha -3.57729975 -3.44062084 -3.18630558
beta 0.01160923 0.01258724 0.01463712
y_pred[1] 0.00000000 0.00000000 1.00000000
y_pred[2] 0.00000000 0.00000000 1.00000000
y_pred[3] 0.00000000 0.00000000 1.00000000
y_pred[4] 0.00000000 0.00000000 1.00000000
y_pred[5] 0.00000000 0.00000000 1.00000000
y_pred[6] 0.00000000 0.00000000 1.00000000
y_pred[7] 0.00000000 0.00000000 1.00000000
y_pred[8] 0.00000000 0.00000000 1.00000000
y_pred[9] 0.00000000 0.00000000 1.00000000
y_pred[10] 0.00000000 0.00000000 1.00000000
y_pred[11] 0.00000000 0.00000000 1.00000000
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y_pred[13] 0.00000000 0.00000000 1.00000000
y_pred[14] 0.00000000 0.00000000 1.00000000
y_pred[15] 0.00000000 0.00000000 1.00000000
y_pred[16] 0.00000000 0.00000000 1.00000000
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y_pred[18] 0.00000000 0.00000000 1.00000000
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y_pred[22] 0.00000000 0.00000000 1.00000000
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y_pred[25] 0.00000000 0.00000000 1.00000000
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y_pred[27] 0.00000000 0.00000000 1.00000000
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y_pred[31] 0.00000000 0.00000000 1.00000000
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y_pred[35] 0.00000000 0.00000000 1.00000000
y_pred[36] 0.00000000 0.00000000 1.00000000
y_pred[37] 0.00000000 0.00000000 1.00000000
y_pred[38] 0.00000000 0.00000000 1.00000000
y_pred[39] 0.00000000 0.00000000 1.00000000
y_pred[40] 0.00000000 0.00000000 1.00000000
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y_pred[45] 0.00000000 0.00000000 1.00000000
y_pred[46] 0.00000000 0.00000000 1.00000000
y_pred[47] 0.00000000 0.00000000 1.00000000
y_pred[48] 0.00000000 0.00000000 1.00000000
y_pred[49] 0.00000000 0.00000000 1.00000000
y_pred[50] 0.00000000 0.00000000 1.00000000
y_pred[51] 0.00000000 0.00000000 1.00000000
y_pred[52] 0.00000000 0.00000000 1.00000000
y_pred[53] 0.00000000 0.00000000 1.00000000
y_pred[54] 0.00000000 0.00000000 1.00000000
y_pred[55] 0.00000000 0.00000000 1.00000000
y_pred[56] 0.00000000 0.00000000 1.00000000
y_pred[57] 0.00000000 0.00000000 1.00000000
y_pred[58] 0.00000000 0.00000000 1.00000000
y_pred[59] 0.00000000 0.00000000 1.00000000
y_pred[60] 0.00000000 0.00000000 1.00000000
y_pred[61] 0.00000000 0.00000000 1.00000000
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y_pred[64] 0.00000000 0.00000000 1.00000000
y_pred[65] 0.00000000 0.00000000 1.00000000
y_pred[66] 0.00000000 0.00000000 1.00000000
y_pred[67] 0.00000000 0.00000000 1.00000000
y_pred[68] 0.00000000 0.00000000 1.00000000
y_pred[69] 0.00000000 0.00000000 1.00000000
y_pred[70] 0.00000000 0.00000000 1.00000000
y_pred[71] 0.00000000 0.00000000 1.00000000
y_pred[72] 0.00000000 0.00000000 1.00000000
y_pred[73] 0.00000000 0.00000000 1.00000000
y_pred[74] 0.00000000 0.00000000 1.00000000
y_pred[75] 0.00000000 0.00000000 1.00000000
y_pred[76] 0.00000000 0.00000000 1.00000000
y_pred[77] 0.00000000 0.00000000 1.00000000
y_pred[78] 0.00000000 0.00000000 1.00000000
y_pred[79] 0.00000000 0.00000000 1.00000000
y_pred[80] 0.00000000 0.00000000 1.00000000
y_pred[81] 0.00000000 0.00000000 1.00000000
y_pred[82] 0.00000000 0.00000000 1.00000000
y_pred[83] 0.00000000 0.00000000 1.00000000
y_pred[84] 0.00000000 0.00000000 1.00000000
y_pred[85] 0.00000000 0.00000000 1.00000000
y_pred[86] 0.00000000 0.00000000 1.00000000
y_pred[87] 0.00000000 0.00000000 1.00000000
y_pred[88] 0.00000000 0.00000000 1.00000000
y_pred[89] 0.00000000 0.00000000 1.00000000
y_pred[90] 0.00000000 0.00000000 1.00000000
y_pred[91] 0.00000000 0.00000000 1.00000000
y_pred[92] 0.00000000 0.00000000 1.00000000
y_pred[93] 0.00000000 0.00000000 1.00000000
y_pred[94] 0.00000000 0.00000000 1.00000000
y_pred[95] 0.00000000 0.00000000 1.00000000
y_pred[96] 0.00000000 0.00000000 1.00000000
y_pred[97] 0.00000000 0.00000000 1.00000000
y_pred[98] 0.00000000 0.00000000 1.00000000
y_pred[99] 0.00000000 0.00000000 1.00000000
y_pred[100] 0.00000000 0.00000000 1.00000000
lp__ -160.78964362 -160.37726134 -160.10980101
# Extraer las estimaciones de los parámetros <- extract (fit_mortality)<- estimaciones_mortality$ alpha<- estimaciones_mortality$ beta# Extraer las predicciones generadas por el modelo para los nuevos mineros <- estimaciones_mortality$ y_pred# Calcular la media y la desviación estándar de las predicciones para nuevos mineros <- colMeans (y_pred_mortality)<- apply (y_pred_mortality, 2 , sd)# Mostrar los resultados para los nuevos mineros cat ("La media predictiva de muertes para nuevos mineros es:" , mean (mean_pred_mortality), " \n " )
La media predictiva de muertes para nuevos mineros es: 0.223392
cat ("La desviación estándar predictiva de muertes para nuevos mineros es:" , mean (sd_pred_mortality), " \n " )
La desviación estándar predictiva de muertes para nuevos mineros es: 0.4165162
Gráficas e Interpretación:
# Trace plot de las cadenas MCMC para beta0 y beta1 mcmc_trace (as.array (fit_mortality), pars = c ("alpha" , "beta" ))# Densidades posteriores de alpha y beta mcmc_dens_overlay (as.array (fit_mortality), pars = c ("alpha" , "beta" ))# Relación entre tiempo de exposición y probabilidad de muerte ggplot (datos_mortality, aes (x = x, y = y/ n)) + geom_point () + stat_smooth (method = "glm" , method.args = list (family = "binomial" ), se = FALSE )
`geom_smooth()` using formula = 'y ~ x'
Warning in eval(family$initialize): non-integer #successes in a binomial glm!
# Intervalos de credibilidad para alpha y beta mcmc_intervals (as.array (fit_mortality), pars = c ("alpha" , "beta" ))
Interpretación de alpha (Intercepto): La estimación para alpha está ajustada alrededor de cero con un intervalo confiable y estrecho, lo que implica que el riesgo inicial de fallecimiento, independiente del tiempo de exposición, es mínimo y se ha determinado con alta precisión en el modelo.
Interpretación de beta (Pendiente): Beta se estima también en torno a cero y su intervalo de credibilidad es reducido, señalando una ausencia de influencia significativa del tiempo de exposición sobre la probabilidad de muerte, basado en el espectro de exposición presente en los datos. Esta estimación de pendiente se calcula con gran exactitud.
Predicciones del Modelo: La media predictiva de muertes es de cerca de 0.223, lo que refleja la expectativa del modelo de que, de cada 100 mineros expuestos 200 horas al mineral, alrededor de 22 podrían fallecer, según los datos históricos y las suposiciones del modelo. La desviación estándar predictiva baja de 0.416 comunica una fuerte seguridad en la media calculada y una variabilidad baja en las proyecciones de muertes del modelo.
# PPC # Extraer las muestras de los parámetros del modelo <- extract (fit_mortality)# Definir la función inv_logit <- function (x) {exp (x) / (1 + exp (x))# Generar predicciones posteriores para cada observación <- length (datos_mortality$ y) # Número de observaciones <- dim (samples$ alpha)[1 ] # Número de muestras en la cadena MCMC <- matrix (NA , nrow = n_obs, ncol = n_samples) # Matriz para almacenar predicciones for (i in 1 : n_samples) {<- samples$ alpha[i] + samples$ beta[i] * datos_mortality$ x<- rbinom (n_obs, datos_mortality$ n, inv_logit (mu)) # Muestreo de distribución binomial usando inversa de la función logit # Calcular la media de las predicciones <- apply (yrep, 1 , mean)# Asegúrate de que 'datos_mortality$y' y 'predicciones_media' tienen la misma longitud if (length (datos_mortality$ y) == length (predicciones_media)) {# Crea el gráfico de dispersión plot (datos_mortality$ y, predicciones_media,xlab = "Valores Observados" ,ylab = "Media de Valores Predichos" ,main = "PPC: Valores Observados vs. Media de Valores Predichos" )# Añade la línea roja usando abline() abline (a = 0 , b = 1 , col = "red" )else {stop ("La longitud de los datos observados y las predicciones no coincide." )
El gráfico muestra cómo se comparan las muertes observadas con las predicciones del modelo. La mayoría de los puntos están cerca de la línea roja, lo que indica una buena concordancia entre los valores observados y predichos. Sin embargo, hay algunas desviaciones, lo que sugiere que el modelo podría mejorarse en ciertas áreas.
Parte 2: “inciso a”
Inciso i)
# install.packages(boot) library (boot)
Attaching package: 'boot'
The following object is masked from 'package:rstanarm':
logit
# Cargar datos data (coal)# Convertir las fechas de 'coal' en años y contar los desastres por año <- floor (coal) # 'coal' es un vector <- table (year) # Conteo de desastres por año # Crear el vector de años y el vector de conteos <- as.numeric (names (disasters))<- as.numeric (disasters)# Gráfico de dispersión plot (years, counts, type = "p" , col = "blue" , xlab = "Año" , ylab = "Número de desastres" ,main = "Número de desastres por año" )# Compilar y ajustar el modelo de Stan <- stan_model (file = "Ej5-modelo2.stan" )<- sampling (stan_model_muertes, data = list (N = length (counts), y = counts, x = years), iter = 10000 , chains = 4 )
SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
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Chain 4: Rejecting initial value:
Chain 4: Log probability evaluates to log(0), i.e. negative infinity.
Chain 4: Stan can't start sampling from this initial value.
Chain 4: Rejecting initial value:
Chain 4: Log probability evaluates to log(0), i.e. negative infinity.
Chain 4: Stan can't start sampling from this initial value.
Chain 4:
Chain 4: Gradient evaluation took 5e-06 seconds
Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.05 seconds.
Chain 4: Adjust your expectations accordingly!
Chain 4:
Chain 4:
Chain 4: Iteration: 1 / 10000 [ 0%] (Warmup)
Chain 4: Iteration: 1000 / 10000 [ 10%] (Warmup)
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Chain 4: Iteration: 5000 / 10000 [ 50%] (Warmup)
Chain 4: Iteration: 5001 / 10000 [ 50%] (Sampling)
Chain 4: Iteration: 6000 / 10000 [ 60%] (Sampling)
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Chain 4: Iteration: 9000 / 10000 [ 90%] (Sampling)
Chain 4: Iteration: 10000 / 10000 [100%] (Sampling)
Chain 4:
Chain 4: Elapsed Time: 3.043 seconds (Warm-up)
Chain 4: 3.304 seconds (Sampling)
Chain 4: 6.347 seconds (Total)
Chain 4:
# Ver los resultados del modelo print (fit_muertes)
Inference for Stan model: anon_model.
4 chains, each with iter=10000; warmup=5000; thin=1;
post-warmup draws per chain=5000, total post-warmup draws=20000.
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
alpha 22.80 0.10 4.82 13.70 19.46 22.73 26.08 32.49 2514 1
beta -0.01 0.00 0.00 -0.02 -0.01 -0.01 -0.01 -0.01 2513 1
y_pred[1] 3.99 0.02 2.04 1.00 3.00 4.00 5.00 8.00 16646 1
y_pred[2] 3.92 0.02 2.05 1.00 2.00 4.00 5.00 8.00 15520 1
y_pred[3] 3.87 0.01 2.03 1.00 2.00 4.00 5.00 8.00 18620 1
y_pred[4] 3.84 0.02 2.01 1.00 2.00 4.00 5.00 8.00 17664 1
y_pred[5] 3.74 0.02 1.99 0.00 2.00 4.00 5.00 8.00 17495 1
y_pred[6] 3.70 0.01 1.96 0.00 2.00 3.00 5.00 8.00 18955 1
y_pred[7] 3.66 0.01 1.96 0.00 2.00 3.00 5.00 8.00 18468 1
y_pred[8] 3.57 0.01 1.92 0.00 2.00 3.00 5.00 8.00 17517 1
y_pred[9] 3.56 0.01 1.92 0.00 2.00 3.00 5.00 8.00 17359 1
y_pred[10] 3.49 0.01 1.89 0.00 2.00 3.00 5.00 8.00 19481 1
y_pred[11] 3.45 0.01 1.88 0.00 2.00 3.00 5.00 8.00 18687 1
y_pred[12] 3.36 0.01 1.85 0.00 2.00 3.00 4.00 7.00 19209 1
y_pred[13] 3.33 0.01 1.85 0.00 2.00 3.00 4.00 7.00 18975 1
y_pred[14] 3.31 0.01 1.84 0.00 2.00 3.00 4.00 7.00 19352 1
y_pred[15] 3.27 0.01 1.84 0.00 2.00 3.00 4.00 7.00 18457 1
y_pred[16] 3.19 0.01 1.81 0.00 2.00 3.00 4.00 7.00 19142 1
y_pred[17] 3.18 0.01 1.79 0.00 2.00 3.00 4.00 7.00 19935 1
y_pred[18] 3.13 0.01 1.79 0.00 2.00 3.00 4.00 7.00 19582 1
y_pred[19] 3.12 0.01 1.78 0.00 2.00 3.00 4.00 7.00 19378 1
y_pred[20] 3.04 0.01 1.76 0.00 2.00 3.00 4.00 7.00 19711 1
y_pred[21] 3.03 0.01 1.76 0.00 2.00 3.00 4.00 7.00 19947 1
y_pred[22] 3.03 0.01 1.76 0.00 2.00 3.00 4.00 7.00 18393 1
y_pred[23] 2.97 0.01 1.75 0.00 2.00 3.00 4.00 7.00 19852 1
y_pred[24] 2.94 0.01 1.72 0.00 2.00 3.00 4.00 7.00 19350 1
y_pred[25] 2.88 0.01 1.70 0.00 2.00 3.00 4.00 7.00 19221 1
y_pred[26] 2.86 0.01 1.72 0.00 2.00 3.00 4.00 7.00 19474 1
y_pred[27] 2.80 0.01 1.69 0.00 2.00 3.00 4.00 7.00 19692 1
y_pred[28] 2.79 0.01 1.69 0.00 2.00 3.00 4.00 7.00 19871 1
y_pred[29] 2.78 0.01 1.69 0.00 2.00 3.00 4.00 6.00 19545 1
y_pred[30] 2.74 0.01 1.67 0.00 2.00 3.00 4.00 6.00 19842 1
y_pred[31] 2.70 0.01 1.64 0.00 2.00 3.00 4.00 6.00 19931 1
y_pred[32] 2.66 0.01 1.63 0.00 1.00 2.00 4.00 6.00 19601 1
y_pred[33] 2.62 0.01 1.65 0.00 1.00 2.00 4.00 6.00 20094 1
y_pred[34] 2.62 0.01 1.62 0.00 1.00 2.00 4.00 6.00 19914 1
y_pred[35] 2.57 0.01 1.62 0.00 1.00 2.00 4.00 6.00 20320 1
y_pred[36] 2.55 0.01 1.60 0.00 1.00 2.00 4.00 6.00 19778 1
y_pred[37] 2.50 0.01 1.60 0.00 1.00 2.00 3.00 6.00 19571 1
y_pred[38] 2.49 0.01 1.59 0.00 1.00 2.00 3.00 6.00 19647 1
y_pred[39] 2.46 0.01 1.59 0.00 1.00 2.00 3.00 6.00 20073 1
y_pred[40] 2.41 0.01 1.56 0.00 1.00 2.00 3.00 6.00 19843 1
y_pred[41] 2.41 0.01 1.57 0.00 1.00 2.00 3.00 6.00 19759 1
y_pred[42] 2.37 0.01 1.55 0.00 1.00 2.00 3.00 6.00 19334 1
y_pred[43] 2.35 0.01 1.54 0.00 1.00 2.00 3.00 6.00 19994 1
y_pred[44] 2.26 0.01 1.50 0.00 1.00 2.00 3.00 6.00 20127 1
y_pred[45] 2.22 0.01 1.50 0.00 1.00 2.00 3.00 6.00 20102 1
y_pred[46] 2.19 0.01 1.48 0.00 1.00 2.00 3.00 5.00 19534 1
y_pred[47] 2.12 0.01 1.47 0.00 1.00 2.00 3.00 5.00 19176 1
y_pred[48] 2.10 0.01 1.46 0.00 1.00 2.00 3.00 5.00 18969 1
y_pred[49] 2.04 0.01 1.43 0.00 1.00 2.00 3.00 5.00 19767 1
y_pred[50] 2.04 0.01 1.44 0.00 1.00 2.00 3.00 5.00 19679 1
y_pred[51] 2.00 0.01 1.42 0.00 1.00 2.00 3.00 5.00 19898 1
y_pred[52] 1.95 0.01 1.41 0.00 1.00 2.00 3.00 5.00 19821 1
y_pred[53] 1.94 0.01 1.40 0.00 1.00 2.00 3.00 5.00 19609 1
y_pred[54] 1.89 0.01 1.38 0.00 1.00 2.00 3.00 5.00 18568 1
y_pred[55] 1.86 0.01 1.38 0.00 1.00 2.00 3.00 5.00 18921 1
y_pred[56] 1.80 0.01 1.35 0.00 1.00 2.00 3.00 5.00 18761 1
y_pred[57] 1.73 0.01 1.34 0.00 1.00 2.00 2.00 5.00 18917 1
y_pred[58] 1.69 0.01 1.31 0.00 1.00 1.50 2.00 5.00 19234 1
y_pred[59] 1.65 0.01 1.30 0.00 1.00 1.00 2.00 5.00 19298 1
y_pred[60] 1.64 0.01 1.29 0.00 1.00 1.00 2.00 5.00 17661 1
y_pred[61] 1.59 0.01 1.28 0.00 1.00 1.00 2.00 4.02 18041 1
y_pred[62] 1.59 0.01 1.27 0.00 1.00 1.00 2.00 4.00 19188 1
y_pred[63] 1.56 0.01 1.27 0.00 1.00 1.00 2.00 4.00 18311 1
y_pred[64] 1.55 0.01 1.26 0.00 1.00 1.00 2.00 4.00 18442 1
y_pred[65] 1.53 0.01 1.25 0.00 1.00 1.00 2.00 4.00 17284 1
y_pred[66] 1.50 0.01 1.24 0.00 1.00 1.00 2.00 4.00 18780 1
y_pred[67] 1.49 0.01 1.23 0.00 1.00 1.00 2.00 4.00 18713 1
y_pred[68] 1.48 0.01 1.23 0.00 1.00 1.00 2.00 4.00 17838 1
y_pred[69] 1.46 0.01 1.23 0.00 1.00 1.00 2.00 4.00 18734 1
y_pred[70] 1.45 0.01 1.21 0.00 1.00 1.00 2.00 4.00 17615 1
y_pred[71] 1.42 0.01 1.21 0.00 1.00 1.00 2.00 4.00 17283 1
y_pred[72] 1.40 0.01 1.20 0.00 0.00 1.00 2.00 4.00 17168 1
y_pred[73] 1.38 0.01 1.18 0.00 0.00 1.00 2.00 4.00 17201 1
y_pred[74] 1.34 0.01 1.18 0.00 0.00 1.00 2.00 4.00 17213 1
y_pred[75] 1.32 0.01 1.18 0.00 0.00 1.00 2.00 4.00 18293 1
y_pred[76] 1.26 0.01 1.14 0.00 0.00 1.00 2.00 4.00 17500 1
y_pred[77] 1.18 0.01 1.11 0.00 0.00 1.00 2.00 4.00 15720 1
y_pred[78] 1.14 0.01 1.09 0.00 0.00 1.00 2.00 4.00 17609 1
y_pred[79] 1.12 0.01 1.08 0.00 0.00 1.00 2.00 4.00 15874 1
lp__ -12.33 0.02 1.02 -15.09 -12.71 -12.03 -11.62 -11.35 3613 1
Samples were drawn using NUTS(diag_e) at Sun Mar 17 13:34:46 2024.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at
convergence, Rhat=1).
$summary
mean se_mean sd 2.5% 25%
alpha 22.79895517 9.609260e-02 4.817717905 13.70060123 19.46471316
beta -0.01157645 5.088415e-05 0.002550714 -0.01671666 -0.01331459
y_pred[1] 3.98650000 1.579152e-02 2.037406514 1.00000000 3.00000000
y_pred[2] 3.92370000 1.643751e-02 2.047751932 1.00000000 2.00000000
y_pred[3] 3.87035000 1.485779e-02 2.027423587 1.00000000 2.00000000
y_pred[4] 3.84330000 1.508650e-02 2.005080080 1.00000000 2.00000000
y_pred[5] 3.74015000 1.507464e-02 1.993897379 0.00000000 2.00000000
y_pred[6] 3.70435000 1.421065e-02 1.956484722 0.00000000 2.00000000
y_pred[7] 3.65685000 1.439509e-02 1.956269262 0.00000000 2.00000000
y_pred[8] 3.57295000 1.449277e-02 1.918140313 0.00000000 2.00000000
y_pred[9] 3.55600000 1.453488e-02 1.915031949 0.00000000 2.00000000
y_pred[10] 3.48510000 1.357360e-02 1.894533571 0.00000000 2.00000000
y_pred[11] 3.45105000 1.374376e-02 1.878770978 0.00000000 2.00000000
y_pred[12] 3.35960000 1.335534e-02 1.850988695 0.00000000 2.00000000
y_pred[13] 3.32930000 1.345100e-02 1.852871600 0.00000000 2.00000000
y_pred[14] 3.30840000 1.323868e-02 1.841645738 0.00000000 2.00000000
y_pred[15] 3.26660000 1.353304e-02 1.838557439 0.00000000 2.00000000
y_pred[16] 3.19320000 1.308516e-02 1.810369474 0.00000000 2.00000000
y_pred[17] 3.17750000 1.270250e-02 1.793503438 0.00000000 2.00000000
y_pred[18] 3.12625000 1.279743e-02 1.790829777 0.00000000 2.00000000
y_pred[19] 3.11660000 1.280519e-02 1.782544056 0.00000000 2.00000000
y_pred[20] 3.03740000 1.254447e-02 1.761208770 0.00000000 2.00000000
y_pred[21] 3.03230000 1.247404e-02 1.761735478 0.00000000 2.00000000
y_pred[22] 3.03180000 1.296325e-02 1.758079436 0.00000000 2.00000000
y_pred[23] 2.97080000 1.239020e-02 1.745737592 0.00000000 2.00000000
y_pred[24] 2.93510000 1.240030e-02 1.724916449 0.00000000 2.00000000
y_pred[25] 2.88205000 1.227828e-02 1.702258113 0.00000000 2.00000000
y_pred[26] 2.86460000 1.235423e-02 1.724040445 0.00000000 2.00000000
y_pred[27] 2.79855000 1.207272e-02 1.694140314 0.00000000 2.00000000
y_pred[28] 2.78855000 1.197874e-02 1.688573795 0.00000000 2.00000000
y_pred[29] 2.78215000 1.205589e-02 1.685447541 0.00000000 2.00000000
y_pred[30] 2.74050000 1.187302e-02 1.672453170 0.00000000 2.00000000
y_pred[31] 2.69985000 1.162352e-02 1.640973680 0.00000000 2.00000000
y_pred[32] 2.66300000 1.167085e-02 1.633941397 0.00000000 1.00000000
y_pred[33] 2.62435000 1.160702e-02 1.645318337 0.00000000 1.00000000
y_pred[34] 2.61910000 1.150980e-02 1.624237389 0.00000000 1.00000000
y_pred[35] 2.57375000 1.133428e-02 1.615670591 0.00000000 1.00000000
y_pred[36] 2.54515000 1.138045e-02 1.600465417 0.00000000 1.00000000
y_pred[37] 2.50225000 1.141195e-02 1.596471852 0.00000000 1.00000000
y_pred[38] 2.48665000 1.135982e-02 1.592277785 0.00000000 1.00000000
y_pred[39] 2.46145000 1.118852e-02 1.585193849 0.00000000 1.00000000
y_pred[40] 2.41195000 1.108299e-02 1.561207567 0.00000000 1.00000000
y_pred[41] 2.40690000 1.115709e-02 1.568328847 0.00000000 1.00000000
y_pred[42] 2.37225000 1.113528e-02 1.548321608 0.00000000 1.00000000
y_pred[43] 2.34755000 1.092258e-02 1.544466985 0.00000000 1.00000000
y_pred[44] 2.26280000 1.056367e-02 1.498648877 0.00000000 1.00000000
y_pred[45] 2.21610000 1.061233e-02 1.504630847 0.00000000 1.00000000
y_pred[46] 2.18805000 1.055444e-02 1.475125756 0.00000000 1.00000000
y_pred[47] 2.12155000 1.059064e-02 1.466554853 0.00000000 1.00000000
y_pred[48] 2.10185000 1.059478e-02 1.459206305 0.00000000 1.00000000
y_pred[49] 2.03820000 1.020598e-02 1.434901985 0.00000000 1.00000000
y_pred[50] 2.04340000 1.024804e-02 1.437609048 0.00000000 1.00000000
y_pred[51] 1.99845000 1.008999e-02 1.423288054 0.00000000 1.00000000
y_pred[52] 1.94970000 9.995903e-03 1.407291346 0.00000000 1.00000000
y_pred[53] 1.93540000 1.002937e-02 1.404430654 0.00000000 1.00000000
y_pred[54] 1.89440000 1.016336e-02 1.384898746 0.00000000 1.00000000
y_pred[55] 1.85595000 1.002546e-02 1.379055723 0.00000000 1.00000000
y_pred[56] 1.80425000 9.871823e-03 1.352155078 0.00000000 1.00000000
y_pred[57] 1.73490000 9.762754e-03 1.342762876 0.00000000 1.00000000
y_pred[58] 1.68740000 9.470825e-03 1.313494387 0.00000000 1.00000000
y_pred[59] 1.65040000 9.378483e-03 1.302829501 0.00000000 1.00000000
y_pred[60] 1.63960000 9.741509e-03 1.294602503 0.00000000 1.00000000
y_pred[61] 1.58900000 9.526337e-03 1.279554947 0.00000000 1.00000000
y_pred[62] 1.58515000 9.183229e-03 1.272057540 0.00000000 1.00000000
y_pred[63] 1.55925000 9.371392e-03 1.268136367 0.00000000 1.00000000
y_pred[64] 1.54555000 9.257850e-03 1.257220835 0.00000000 1.00000000
y_pred[65] 1.53065000 9.500852e-03 1.249055077 0.00000000 1.00000000
y_pred[66] 1.50200000 9.084569e-03 1.244939153 0.00000000 1.00000000
y_pred[67] 1.48950000 9.013669e-03 1.233031130 0.00000000 1.00000000
y_pred[68] 1.47710000 9.245398e-03 1.234808417 0.00000000 1.00000000
y_pred[69] 1.45915000 8.980369e-03 1.229148818 0.00000000 1.00000000
y_pred[70] 1.45490000 9.141800e-03 1.213317599 0.00000000 1.00000000
y_pred[71] 1.41890000 9.229129e-03 1.213299796 0.00000000 1.00000000
y_pred[72] 1.39855000 9.189073e-03 1.204026736 0.00000000 0.00000000
y_pred[73] 1.37620000 9.016016e-03 1.182473455 0.00000000 0.00000000
y_pred[74] 1.34000000 9.001959e-03 1.181046038 0.00000000 0.00000000
y_pred[75] 1.31580000 8.699564e-03 1.176622107 0.00000000 0.00000000
y_pred[76] 1.25625000 8.652599e-03 1.144618471 0.00000000 0.00000000
y_pred[77] 1.17675000 8.831049e-03 1.107235628 0.00000000 0.00000000
y_pred[78] 1.13695000 8.177947e-03 1.085197484 0.00000000 0.00000000
y_pred[79] 1.11520000 8.590615e-03 1.082352777 0.00000000 0.00000000
lp__ -12.33227107 1.691460e-02 1.016768243 -15.09346922 -12.70708288
50% 75% 97.5% n_eff Rhat
alpha 22.72926984 26.082481677 32.491124480 2513.639 1.0007614
beta -0.01153511 -0.009813334 -0.006749275 2512.803 1.0007666
y_pred[1] 4.00000000 5.000000000 8.000000000 16645.903 1.0000521
y_pred[2] 4.00000000 5.000000000 8.000000000 15519.680 0.9999331
y_pred[3] 4.00000000 5.000000000 8.000000000 18620.050 0.9998647
y_pred[4] 4.00000000 5.000000000 8.000000000 17663.885 1.0001507
y_pred[5] 4.00000000 5.000000000 8.000000000 17494.909 0.9999916
y_pred[6] 3.00000000 5.000000000 8.000000000 18955.055 1.0000450
y_pred[7] 3.00000000 5.000000000 8.000000000 18468.370 0.9999204
y_pred[8] 3.00000000 5.000000000 8.000000000 17516.934 0.9999414
y_pred[9] 3.00000000 5.000000000 8.000000000 17359.188 0.9999203
y_pred[10] 3.00000000 5.000000000 8.000000000 19481.161 1.0000067
y_pred[11] 3.00000000 5.000000000 8.000000000 18686.856 0.9999681
y_pred[12] 3.00000000 4.000000000 7.000000000 19208.694 0.9998940
y_pred[13] 3.00000000 4.000000000 7.000000000 18974.993 0.9999770
y_pred[14] 3.00000000 4.000000000 7.000000000 19351.870 0.9999754
y_pred[15] 3.00000000 4.000000000 7.000000000 18457.109 1.0001338
y_pred[16] 3.00000000 4.000000000 7.000000000 19141.520 1.0000919
y_pred[17] 3.00000000 4.000000000 7.000000000 19935.440 1.0000306
y_pred[18] 3.00000000 4.000000000 7.000000000 19582.283 1.0001373
y_pred[19] 3.00000000 4.000000000 7.000000000 19377.986 1.0000039
y_pred[20] 3.00000000 4.000000000 7.000000000 19711.372 1.0000026
y_pred[21] 3.00000000 4.000000000 7.000000000 19946.527 1.0000590
y_pred[22] 3.00000000 4.000000000 7.000000000 18392.864 0.9999834
y_pred[23] 3.00000000 4.000000000 7.000000000 19851.866 1.0000471
y_pred[24] 3.00000000 4.000000000 7.000000000 19349.594 1.0001104
y_pred[25] 3.00000000 4.000000000 7.000000000 19220.992 0.9998832
y_pred[26] 3.00000000 4.000000000 7.000000000 19474.388 1.0000829
y_pred[27] 3.00000000 4.000000000 7.000000000 19691.926 1.0000194
y_pred[28] 3.00000000 4.000000000 7.000000000 19870.908 1.0000199
y_pred[29] 3.00000000 4.000000000 6.000000000 19544.830 1.0000401
y_pred[30] 3.00000000 4.000000000 6.000000000 19842.017 0.9999271
y_pred[31] 3.00000000 4.000000000 6.000000000 19930.942 1.0001339
y_pred[32] 2.00000000 4.000000000 6.000000000 19600.538 0.9998955
y_pred[33] 2.00000000 4.000000000 6.000000000 20093.637 0.9998730
y_pred[34] 2.00000000 4.000000000 6.000000000 19914.232 0.9998751
y_pred[35] 2.00000000 4.000000000 6.000000000 20319.732 1.0000219
y_pred[36] 2.00000000 4.000000000 6.000000000 19777.616 0.9998565
y_pred[37] 2.00000000 3.000000000 6.000000000 19570.544 1.0000296
y_pred[38] 2.00000000 3.000000000 6.000000000 19646.948 1.0000768
y_pred[39] 2.00000000 3.000000000 6.000000000 20073.332 0.9999936
y_pred[40] 2.00000000 3.000000000 6.000000000 19843.009 0.9999982
y_pred[41] 2.00000000 3.000000000 6.000000000 19759.354 1.0000496
y_pred[42] 2.00000000 3.000000000 6.000000000 19333.925 0.9999527
y_pred[43] 2.00000000 3.000000000 6.000000000 19994.309 0.9998864
y_pred[44] 2.00000000 3.000000000 6.000000000 20126.592 1.0000554
y_pred[45] 2.00000000 3.000000000 6.000000000 20101.974 0.9998914
y_pred[46] 2.00000000 3.000000000 5.000000000 19533.837 1.0001169
y_pred[47] 2.00000000 3.000000000 5.000000000 19175.748 0.9998658
y_pred[48] 2.00000000 3.000000000 5.000000000 18969.228 1.0000032
y_pred[49] 2.00000000 3.000000000 5.000000000 19766.730 1.0000953
y_pred[50] 2.00000000 3.000000000 5.000000000 19678.879 1.0000193
y_pred[51] 2.00000000 3.000000000 5.000000000 19897.756 1.0001551
y_pred[52] 2.00000000 3.000000000 5.000000000 19820.926 1.0002192
y_pred[53] 2.00000000 3.000000000 5.000000000 19608.895 1.0000498
y_pred[54] 2.00000000 3.000000000 5.000000000 18567.829 1.0000710
y_pred[55] 2.00000000 3.000000000 5.000000000 18921.475 0.9999199
y_pred[56] 2.00000000 3.000000000 5.000000000 18761.101 1.0001549
y_pred[57] 2.00000000 2.000000000 5.000000000 18917.072 1.0000610
y_pred[58] 1.50000000 2.000000000 5.000000000 19234.495 1.0000527
y_pred[59] 1.00000000 2.000000000 5.000000000 19297.898 1.0004642
y_pred[60] 1.00000000 2.000000000 5.000000000 17661.209 1.0000289
y_pred[61] 1.00000000 2.000000000 4.025000000 18041.223 1.0002414
y_pred[62] 1.00000000 2.000000000 4.000000000 19187.688 0.9998948
y_pred[63] 1.00000000 2.000000000 4.000000000 18311.492 1.0000434
y_pred[64] 1.00000000 2.000000000 4.000000000 18441.782 1.0000560
y_pred[65] 1.00000000 2.000000000 4.000000000 17283.756 0.9999386
y_pred[66] 1.00000000 2.000000000 4.000000000 18779.654 0.9999644
y_pred[67] 1.00000000 2.000000000 4.000000000 18713.061 1.0001819
y_pred[68] 1.00000000 2.000000000 4.000000000 17838.073 1.0000011
y_pred[69] 1.00000000 2.000000000 4.000000000 18733.570 1.0000175
y_pred[70] 1.00000000 2.000000000 4.000000000 17615.119 0.9998457
y_pred[71] 1.00000000 2.000000000 4.000000000 17282.829 1.0002552
y_pred[72] 1.00000000 2.000000000 4.000000000 17168.360 0.9999690
y_pred[73] 1.00000000 2.000000000 4.000000000 17200.992 1.0001445
y_pred[74] 1.00000000 2.000000000 4.000000000 17213.121 1.0000215
y_pred[75] 1.00000000 2.000000000 4.000000000 18292.750 0.9999828
y_pred[76] 1.00000000 2.000000000 4.000000000 17499.609 1.0000296
y_pred[77] 1.00000000 2.000000000 4.000000000 15720.108 0.9998241
y_pred[78] 1.00000000 2.000000000 4.000000000 17608.768 0.9999903
y_pred[79] 1.00000000 2.000000000 4.000000000 15874.101 1.0001439
lp__ -12.02559630 -11.615723032 -11.347852077 3613.439 1.0007848
$c_summary
, , chains = chain:1
stats
parameter mean sd 2.5% 25% 50%
alpha 22.97985856 4.740681068 14.28002956 19.65351995 22.75931684
beta -0.01167162 0.002510009 -0.01703753 -0.01342365 -0.01155592
y_pred[1] 3.96680000 2.040816196 1.00000000 3.00000000 4.00000000
y_pred[2] 3.94100000 2.077397920 1.00000000 2.00000000 4.00000000
y_pred[3] 3.89100000 2.038025935 1.00000000 2.00000000 4.00000000
y_pred[4] 3.84720000 2.015605292 1.00000000 2.00000000 4.00000000
y_pred[5] 3.76380000 1.996899367 0.00000000 2.00000000 4.00000000
y_pred[6] 3.73740000 1.963061885 1.00000000 2.00000000 4.00000000
y_pred[7] 3.68020000 1.947379372 0.00000000 2.00000000 4.00000000
y_pred[8] 3.55920000 1.914583110 0.00000000 2.00000000 3.00000000
y_pred[9] 3.56820000 1.918563248 0.00000000 2.00000000 3.00000000
y_pred[10] 3.48940000 1.893516496 0.00000000 2.00000000 3.00000000
y_pred[11] 3.46680000 1.875206933 0.00000000 2.00000000 3.00000000
y_pred[12] 3.36960000 1.859163021 0.00000000 2.00000000 3.00000000
y_pred[13] 3.34940000 1.845968895 0.00000000 2.00000000 3.00000000
y_pred[14] 3.28400000 1.828992357 0.00000000 2.00000000 3.00000000
y_pred[15] 3.25600000 1.855681199 0.00000000 2.00000000 3.00000000
y_pred[16] 3.22740000 1.803091642 0.00000000 2.00000000 3.00000000
y_pred[17] 3.20580000 1.767956870 0.00000000 2.00000000 3.00000000
y_pred[18] 3.19020000 1.796181843 0.00000000 2.00000000 3.00000000
y_pred[19] 3.08920000 1.771177793 0.00000000 2.00000000 3.00000000
y_pred[20] 3.06000000 1.787691016 0.00000000 2.00000000 3.00000000
y_pred[21] 3.07420000 1.750687677 0.00000000 2.00000000 3.00000000
y_pred[22] 3.03980000 1.770322787 0.00000000 2.00000000 3.00000000
y_pred[23] 2.95460000 1.725785186 0.00000000 2.00000000 3.00000000
y_pred[24] 2.90120000 1.715467028 0.00000000 2.00000000 3.00000000
y_pred[25] 2.88840000 1.702388048 0.00000000 2.00000000 3.00000000
y_pred[26] 2.90520000 1.709385082 0.00000000 2.00000000 3.00000000
y_pred[27] 2.79580000 1.679960361 0.00000000 2.00000000 3.00000000
y_pred[28] 2.79060000 1.700155800 0.00000000 2.00000000 3.00000000
y_pred[29] 2.80860000 1.681467070 0.00000000 2.00000000 3.00000000
y_pred[30] 2.74500000 1.663889631 0.00000000 2.00000000 3.00000000
y_pred[31] 2.72640000 1.640512510 0.00000000 2.00000000 3.00000000
y_pred[32] 2.65020000 1.623442969 0.00000000 1.00000000 2.00000000
y_pred[33] 2.63280000 1.638200507 0.00000000 1.00000000 2.00000000
y_pred[34] 2.60160000 1.601183999 0.00000000 1.00000000 2.00000000
y_pred[35] 2.57880000 1.634235205 0.00000000 1.00000000 2.00000000
y_pred[36] 2.54920000 1.590121083 0.00000000 1.00000000 2.00000000
y_pred[37] 2.48700000 1.592211678 0.00000000 1.00000000 2.00000000
y_pred[38] 2.50800000 1.602763167 0.00000000 1.00000000 2.00000000
y_pred[39] 2.49720000 1.590376691 0.00000000 1.00000000 2.00000000
y_pred[40] 2.42800000 1.566175782 0.00000000 1.00000000 2.00000000
y_pred[41] 2.42980000 1.577456698 0.00000000 1.00000000 2.00000000
y_pred[42] 2.35440000 1.528289166 0.00000000 1.00000000 2.00000000
y_pred[43] 2.37240000 1.537722718 0.00000000 1.00000000 2.00000000
y_pred[44] 2.23400000 1.488384042 0.00000000 1.00000000 2.00000000
y_pred[45] 2.22220000 1.516076138 0.00000000 1.00000000 2.00000000
y_pred[46] 2.14920000 1.458000176 0.00000000 1.00000000 2.00000000
y_pred[47] 2.11620000 1.480789015 0.00000000 1.00000000 2.00000000
y_pred[48] 2.11200000 1.473326216 0.00000000 1.00000000 2.00000000
y_pred[49] 2.03540000 1.412425513 0.00000000 1.00000000 2.00000000
y_pred[50] 2.04580000 1.410992750 0.00000000 1.00000000 2.00000000
y_pred[51] 1.98020000 1.435764690 0.00000000 1.00000000 2.00000000
y_pred[52] 1.97940000 1.418653642 0.00000000 1.00000000 2.00000000
y_pred[53] 1.90680000 1.387695536 0.00000000 1.00000000 2.00000000
y_pred[54] 1.88240000 1.369578544 0.00000000 1.00000000 2.00000000
y_pred[55] 1.84640000 1.381444432 0.00000000 1.00000000 2.00000000
y_pred[56] 1.81180000 1.349498051 0.00000000 1.00000000 2.00000000
y_pred[57] 1.72240000 1.350445475 0.00000000 1.00000000 2.00000000
y_pred[58] 1.66400000 1.307916713 0.00000000 1.00000000 1.00000000
y_pred[59] 1.62860000 1.282416063 0.00000000 1.00000000 1.00000000
y_pred[60] 1.66140000 1.298571252 0.00000000 1.00000000 1.00000000
y_pred[61] 1.58440000 1.282811662 0.00000000 1.00000000 1.00000000
y_pred[62] 1.58320000 1.278203630 0.00000000 1.00000000 1.00000000
y_pred[63] 1.54920000 1.248795923 0.00000000 1.00000000 1.00000000
y_pred[64] 1.52040000 1.240278799 0.00000000 1.00000000 1.00000000
y_pred[65] 1.54760000 1.270140501 0.00000000 1.00000000 1.00000000
y_pred[66] 1.50340000 1.242697590 0.00000000 1.00000000 1.00000000
y_pred[67] 1.52820000 1.233332470 0.00000000 1.00000000 1.00000000
y_pred[68] 1.46140000 1.225891758 0.00000000 1.00000000 1.00000000
y_pred[69] 1.43480000 1.225744447 0.00000000 1.00000000 1.00000000
y_pred[70] 1.44840000 1.203838563 0.00000000 1.00000000 1.00000000
y_pred[71] 1.42300000 1.209778373 0.00000000 1.00000000 1.00000000
y_pred[72] 1.38820000 1.212185893 0.00000000 0.00000000 1.00000000
y_pred[73] 1.34760000 1.161827960 0.00000000 0.00000000 1.00000000
y_pred[74] 1.34740000 1.188526718 0.00000000 0.00000000 1.00000000
y_pred[75] 1.32400000 1.180890723 0.00000000 0.00000000 1.00000000
y_pred[76] 1.23140000 1.128764307 0.00000000 0.00000000 1.00000000
y_pred[77] 1.17680000 1.078598366 0.00000000 0.00000000 1.00000000
y_pred[78] 1.13420000 1.093814265 0.00000000 0.00000000 1.00000000
y_pred[79] 1.09400000 1.052703965 0.00000000 0.00000000 1.00000000
lp__ -12.31977386 0.978067911 -14.91043681 -12.70612048 -12.01334101
stats
parameter 75% 97.5%
alpha 26.285745065 33.07249683
beta -0.009906864 -0.00703935
y_pred[1] 5.000000000 8.00000000
y_pred[2] 5.000000000 8.00000000
y_pred[3] 5.000000000 8.00000000
y_pred[4] 5.000000000 8.00000000
y_pred[5] 5.000000000 8.00000000
y_pred[6] 5.000000000 8.00000000
y_pred[7] 5.000000000 8.00000000
y_pred[8] 5.000000000 8.00000000
y_pred[9] 5.000000000 8.00000000
y_pred[10] 5.000000000 8.00000000
y_pred[11] 5.000000000 8.00000000
y_pred[12] 4.000000000 7.00000000
y_pred[13] 5.000000000 7.00000000
y_pred[14] 4.000000000 7.00000000
y_pred[15] 4.000000000 7.00000000
y_pred[16] 4.000000000 7.00000000
y_pred[17] 4.000000000 7.00000000
y_pred[18] 4.000000000 7.00000000
y_pred[19] 4.000000000 7.00000000
y_pred[20] 4.000000000 7.00000000
y_pred[21] 4.000000000 7.00000000
y_pred[22] 4.000000000 7.00000000
y_pred[23] 4.000000000 7.00000000
y_pred[24] 4.000000000 7.00000000
y_pred[25] 4.000000000 7.00000000
y_pred[26] 4.000000000 7.00000000
y_pred[27] 4.000000000 7.00000000
y_pred[28] 4.000000000 7.00000000
y_pred[29] 4.000000000 6.00000000
y_pred[30] 4.000000000 6.00000000
y_pred[31] 4.000000000 6.00000000
y_pred[32] 4.000000000 6.00000000
y_pred[33] 4.000000000 6.00000000
y_pred[34] 4.000000000 6.00000000
y_pred[35] 4.000000000 6.00000000
y_pred[36] 3.000000000 6.00000000
y_pred[37] 3.000000000 6.00000000
y_pred[38] 3.000000000 6.00000000
y_pred[39] 3.000000000 6.00000000
y_pred[40] 3.000000000 6.00000000
y_pred[41] 3.000000000 6.00000000
y_pred[42] 3.000000000 6.00000000
y_pred[43] 3.000000000 6.00000000
y_pred[44] 3.000000000 5.00000000
y_pred[45] 3.000000000 6.00000000
y_pred[46] 3.000000000 5.00000000
y_pred[47] 3.000000000 5.00000000
y_pred[48] 3.000000000 5.00000000
y_pred[49] 3.000000000 5.00000000
y_pred[50] 3.000000000 5.00000000
y_pred[51] 3.000000000 5.00000000
y_pred[52] 3.000000000 5.00000000
y_pred[53] 3.000000000 5.00000000
y_pred[54] 3.000000000 5.00000000
y_pred[55] 3.000000000 5.00000000
y_pred[56] 3.000000000 5.00000000
y_pred[57] 2.000000000 5.00000000
y_pred[58] 2.000000000 5.00000000
y_pred[59] 2.000000000 5.00000000
y_pred[60] 2.000000000 5.00000000
y_pred[61] 2.000000000 4.00000000
y_pred[62] 2.000000000 4.00000000
y_pred[63] 2.000000000 4.00000000
y_pred[64] 2.000000000 4.00000000
y_pred[65] 2.000000000 4.00000000
y_pred[66] 2.000000000 4.00000000
y_pred[67] 2.000000000 4.00000000
y_pred[68] 2.000000000 4.00000000
y_pred[69] 2.000000000 4.00000000
y_pred[70] 2.000000000 4.00000000
y_pred[71] 2.000000000 4.00000000
y_pred[72] 2.000000000 4.00000000
y_pred[73] 2.000000000 4.00000000
y_pred[74] 2.000000000 4.00000000
y_pred[75] 2.000000000 4.00000000
y_pred[76] 2.000000000 4.00000000
y_pred[77] 2.000000000 4.00000000
y_pred[78] 2.000000000 4.00000000
y_pred[79] 2.000000000 4.00000000
lp__ -11.613423519 -11.34407625
, , chains = chain:2
stats
parameter mean sd 2.5% 25% 50%
alpha 22.79373662 4.837741182 13.72158594 19.46978705 22.74845418
beta -0.01157397 0.002561543 -0.01667434 -0.01334995 -0.01155324
y_pred[1] 4.04360000 2.044342170 1.00000000 3.00000000 4.00000000
y_pred[2] 3.88600000 2.046128375 0.00000000 2.00000000 4.00000000
y_pred[3] 3.84140000 2.001761087 1.00000000 2.00000000 4.00000000
y_pred[4] 3.85120000 1.978747495 1.00000000 2.00000000 4.00000000
y_pred[5] 3.76000000 1.995594267 0.00000000 2.00000000 4.00000000
y_pred[6] 3.67160000 1.939099136 0.00000000 2.00000000 3.00000000
y_pred[7] 3.62160000 1.970479637 0.00000000 2.00000000 3.00000000
y_pred[8] 3.55320000 1.911517863 0.00000000 2.00000000 3.00000000
y_pred[9] 3.55600000 1.920833652 0.00000000 2.00000000 3.00000000
y_pred[10] 3.46880000 1.906345559 0.00000000 2.00000000 3.00000000
y_pred[11] 3.44280000 1.908469704 0.00000000 2.00000000 3.00000000
y_pred[12] 3.36180000 1.866118228 0.00000000 2.00000000 3.00000000
y_pred[13] 3.36500000 1.886925303 0.00000000 2.00000000 3.00000000
y_pred[14] 3.30660000 1.843387115 0.00000000 2.00000000 3.00000000
y_pred[15] 3.32100000 1.850146915 0.00000000 2.00000000 3.00000000
y_pred[16] 3.21880000 1.814823759 0.00000000 2.00000000 3.00000000
y_pred[17] 3.16540000 1.805628671 0.00000000 2.00000000 3.00000000
y_pred[18] 3.12300000 1.797697790 0.00000000 2.00000000 3.00000000
y_pred[19] 3.09460000 1.787929019 0.00000000 2.00000000 3.00000000
y_pred[20] 3.05880000 1.753042267 0.00000000 2.00000000 3.00000000
y_pred[21] 3.00640000 1.760164389 0.00000000 2.00000000 3.00000000
y_pred[22] 3.02760000 1.755521179 0.00000000 2.00000000 3.00000000
y_pred[23] 2.99920000 1.748316528 0.00000000 2.00000000 3.00000000
y_pred[24] 2.95540000 1.737243346 0.00000000 2.00000000 3.00000000
y_pred[25] 2.88380000 1.687266112 0.00000000 2.00000000 3.00000000
y_pred[26] 2.88020000 1.750560154 0.00000000 2.00000000 3.00000000
y_pred[27] 2.81540000 1.710762456 0.00000000 2.00000000 3.00000000
y_pred[28] 2.79380000 1.680430400 0.00000000 2.00000000 3.00000000
y_pred[29] 2.78880000 1.701520965 0.00000000 2.00000000 3.00000000
y_pred[30] 2.74360000 1.681078298 0.00000000 1.00000000 3.00000000
y_pred[31] 2.66420000 1.640480599 0.00000000 1.00000000 2.50000000
y_pred[32] 2.65740000 1.667867380 0.00000000 1.00000000 2.00000000
y_pred[33] 2.62400000 1.644860211 0.00000000 1.00000000 2.00000000
y_pred[34] 2.61460000 1.646392712 0.00000000 1.00000000 2.00000000
y_pred[35] 2.60420000 1.632076927 0.00000000 1.00000000 2.00000000
y_pred[36] 2.55600000 1.606169342 0.00000000 1.00000000 2.00000000
y_pred[37] 2.51940000 1.582189718 0.00000000 1.00000000 2.00000000
y_pred[38] 2.49720000 1.586472672 0.00000000 1.00000000 2.00000000
y_pred[39] 2.45260000 1.565708635 0.00000000 1.00000000 2.00000000
y_pred[40] 2.39720000 1.552003190 0.00000000 1.00000000 2.00000000
y_pred[41] 2.39140000 1.557013455 0.00000000 1.00000000 2.00000000
y_pred[42] 2.35140000 1.551257335 0.00000000 1.00000000 2.00000000
y_pred[43] 2.34180000 1.558672080 0.00000000 1.00000000 2.00000000
y_pred[44] 2.25100000 1.488368922 0.00000000 1.00000000 2.00000000
y_pred[45] 2.23060000 1.501690599 0.00000000 1.00000000 2.00000000
y_pred[46] 2.21240000 1.487322650 0.00000000 1.00000000 2.00000000
y_pred[47] 2.10640000 1.478755011 0.00000000 1.00000000 2.00000000
y_pred[48] 2.12380000 1.477061238 0.00000000 1.00000000 2.00000000
y_pred[49] 2.07960000 1.448338143 0.00000000 1.00000000 2.00000000
y_pred[50] 2.01880000 1.424096967 0.00000000 1.00000000 2.00000000
y_pred[51] 1.95980000 1.389593521 0.00000000 1.00000000 2.00000000
y_pred[52] 1.97020000 1.412554786 0.00000000 1.00000000 2.00000000
y_pred[53] 1.95960000 1.414060732 0.00000000 1.00000000 2.00000000
y_pred[54] 1.89420000 1.385564982 0.00000000 1.00000000 2.00000000
y_pred[55] 1.84260000 1.366967066 0.00000000 1.00000000 2.00000000
y_pred[56] 1.81860000 1.366626347 0.00000000 1.00000000 2.00000000
y_pred[57] 1.77880000 1.347231816 0.00000000 1.00000000 2.00000000
y_pred[58] 1.68040000 1.317498767 0.00000000 1.00000000 1.00000000
y_pred[59] 1.63760000 1.304686430 0.00000000 1.00000000 1.00000000
y_pred[60] 1.64480000 1.294205530 0.00000000 1.00000000 1.00000000
y_pred[61] 1.57300000 1.267198547 0.00000000 1.00000000 1.00000000
y_pred[62] 1.59280000 1.270948946 0.00000000 1.00000000 1.00000000
y_pred[63] 1.56320000 1.272764607 0.00000000 1.00000000 1.00000000
y_pred[64] 1.53980000 1.252808791 0.00000000 1.00000000 1.00000000
y_pred[65] 1.50240000 1.246878174 0.00000000 1.00000000 1.00000000
y_pred[66] 1.48540000 1.235189046 0.00000000 1.00000000 1.00000000
y_pred[67] 1.44880000 1.221833514 0.00000000 1.00000000 1.00000000
y_pred[68] 1.51160000 1.237324385 0.00000000 1.00000000 1.00000000
y_pred[69] 1.46200000 1.227704138 0.00000000 1.00000000 1.00000000
y_pred[70] 1.46560000 1.208928841 0.00000000 1.00000000 1.00000000
y_pred[71] 1.41920000 1.231330417 0.00000000 0.00000000 1.00000000
y_pred[72] 1.39540000 1.192033149 0.00000000 0.00000000 1.00000000
y_pred[73] 1.39140000 1.194860485 0.00000000 0.00000000 1.00000000
y_pred[74] 1.32520000 1.188834566 0.00000000 0.00000000 1.00000000
y_pred[75] 1.30620000 1.172653650 0.00000000 0.00000000 1.00000000
y_pred[76] 1.24960000 1.147154319 0.00000000 0.00000000 1.00000000
y_pred[77] 1.17400000 1.119810160 0.00000000 0.00000000 1.00000000
y_pred[78] 1.11400000 1.080387638 0.00000000 0.00000000 1.00000000
y_pred[79] 1.11140000 1.084262498 0.00000000 0.00000000 1.00000000
lp__ -12.32825424 1.025013831 -15.08590674 -12.69421523 -12.03784797
stats
parameter 75% 97.5%
alpha 26.142847995 32.460796314
beta -0.009815258 -0.006769324
y_pred[1] 5.000000000 9.000000000
y_pred[2] 5.000000000 8.000000000
y_pred[3] 5.000000000 8.000000000
y_pred[4] 5.000000000 8.000000000
y_pred[5] 5.000000000 8.000000000
y_pred[6] 5.000000000 8.000000000
y_pred[7] 5.000000000 8.000000000
y_pred[8] 5.000000000 8.000000000
y_pred[9] 5.000000000 8.000000000
y_pred[10] 5.000000000 8.000000000
y_pred[11] 5.000000000 8.000000000
y_pred[12] 4.000000000 7.000000000
y_pred[13] 5.000000000 8.000000000
y_pred[14] 4.000000000 7.000000000
y_pred[15] 4.000000000 7.000000000
y_pred[16] 4.000000000 7.000000000
y_pred[17] 4.000000000 7.000000000
y_pred[18] 4.000000000 7.000000000
y_pred[19] 4.000000000 7.000000000
y_pred[20] 4.000000000 7.000000000
y_pred[21] 4.000000000 7.000000000
y_pred[22] 4.000000000 7.000000000
y_pred[23] 4.000000000 7.000000000
y_pred[24] 4.000000000 7.000000000
y_pred[25] 4.000000000 7.000000000
y_pred[26] 4.000000000 7.000000000
y_pred[27] 4.000000000 7.000000000
y_pred[28] 4.000000000 6.000000000
y_pred[29] 4.000000000 7.000000000
y_pred[30] 4.000000000 7.000000000
y_pred[31] 4.000000000 6.000000000
y_pred[32] 4.000000000 6.000000000
y_pred[33] 4.000000000 6.000000000
y_pred[34] 4.000000000 6.000000000
y_pred[35] 4.000000000 6.000000000
y_pred[36] 3.000000000 6.000000000
y_pred[37] 3.000000000 6.000000000
y_pred[38] 3.000000000 6.000000000
y_pred[39] 3.000000000 6.000000000
y_pred[40] 3.000000000 6.000000000
y_pred[41] 3.000000000 6.000000000
y_pred[42] 3.000000000 6.000000000
y_pred[43] 3.000000000 6.000000000
y_pred[44] 3.000000000 6.000000000
y_pred[45] 3.000000000 6.000000000
y_pred[46] 3.000000000 5.000000000
y_pred[47] 3.000000000 5.000000000
y_pred[48] 3.000000000 5.000000000
y_pred[49] 3.000000000 5.000000000
y_pred[50] 3.000000000 5.000000000
y_pred[51] 3.000000000 5.000000000
y_pred[52] 3.000000000 5.000000000
y_pred[53] 3.000000000 5.000000000
y_pred[54] 3.000000000 5.000000000
y_pred[55] 3.000000000 5.000000000
y_pred[56] 3.000000000 5.000000000
y_pred[57] 3.000000000 5.000000000
y_pred[58] 2.000000000 5.000000000
y_pred[59] 2.000000000 5.000000000
y_pred[60] 2.000000000 5.000000000
y_pred[61] 2.000000000 4.000000000
y_pred[62] 2.000000000 5.000000000
y_pred[63] 2.000000000 4.000000000
y_pred[64] 2.000000000 4.000000000
y_pred[65] 2.000000000 4.000000000
y_pred[66] 2.000000000 4.000000000
y_pred[67] 2.000000000 4.000000000
y_pred[68] 2.000000000 4.000000000
y_pred[69] 2.000000000 4.000000000
y_pred[70] 2.000000000 4.000000000
y_pred[71] 2.000000000 4.000000000
y_pred[72] 2.000000000 4.000000000
y_pred[73] 2.000000000 4.000000000
y_pred[74] 2.000000000 4.000000000
y_pred[75] 2.000000000 4.000000000
y_pred[76] 2.000000000 4.000000000
y_pred[77] 2.000000000 4.000000000
y_pred[78] 2.000000000 4.000000000
y_pred[79] 2.000000000 4.000000000
lp__ -11.621082136 -11.353400918
, , chains = chain:3
stats
parameter mean sd 2.5% 25% 50%
alpha 22.61805360 4.998767786 12.6612421 18.94296808 22.61231261
beta -0.01147999 0.002645437 -0.0166679 -0.01329615 -0.01148662
y_pred[1] 3.94780000 2.046732269 1.0000000 2.00000000 4.00000000
y_pred[2] 3.91240000 2.062129170 1.0000000 2.00000000 4.00000000
y_pred[3] 3.87160000 2.043415902 0.0000000 2.00000000 4.00000000
y_pred[4] 3.85360000 1.988607038 1.0000000 2.00000000 4.00000000
y_pred[5] 3.72520000 1.984659350 1.0000000 2.00000000 4.00000000
y_pred[6] 3.70480000 1.942887522 1.0000000 2.00000000 4.00000000
y_pred[7] 3.67840000 1.958198240 0.0000000 2.00000000 3.00000000
y_pred[8] 3.57440000 1.903152395 0.0000000 2.00000000 3.00000000
y_pred[9] 3.55360000 1.892575866 0.0000000 2.00000000 3.00000000
y_pred[10] 3.47120000 1.879115956 0.0000000 2.00000000 3.00000000
y_pred[11] 3.41400000 1.881943767 0.0000000 2.00000000 3.00000000
y_pred[12] 3.34660000 1.833995951 0.0000000 2.00000000 3.00000000
y_pred[13] 3.29680000 1.834716053 0.0000000 2.00000000 3.00000000
y_pred[14] 3.31160000 1.841516678 0.0000000 2.00000000 3.00000000
y_pred[15] 3.27240000 1.846965212 0.0000000 2.00000000 3.00000000
y_pred[16] 3.14900000 1.807166891 0.0000000 2.00000000 3.00000000
y_pred[17] 3.14580000 1.816480740 0.0000000 2.00000000 3.00000000
y_pred[18] 3.08880000 1.772326942 0.0000000 2.00000000 3.00000000
y_pred[19] 3.12300000 1.800255311 0.0000000 2.00000000 3.00000000
y_pred[20] 3.04380000 1.758778047 0.0000000 2.00000000 3.00000000
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y_pred[67] 1.49500000 1.237206990 0.0000000 1.00000000 1.00000000
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y_pred[70] 1.45060000 1.225014193 0.0000000 1.00000000 1.00000000
y_pred[71] 1.40640000 1.191773093 0.0000000 1.00000000 1.00000000
y_pred[72] 1.38340000 1.203783311 0.0000000 0.00000000 1.00000000
y_pred[73] 1.39120000 1.186273159 0.0000000 0.00000000 1.00000000
y_pred[74] 1.32960000 1.176282521 0.0000000 0.00000000 1.00000000
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y_pred[77] 1.18300000 1.100069557 0.0000000 0.00000000 1.00000000
y_pred[78] 1.16080000 1.091779170 0.0000000 0.00000000 1.00000000
y_pred[79] 1.13520000 1.095427292 0.0000000 0.00000000 1.00000000
lp__ -12.36443078 1.033548407 -15.1766098 -12.77490309 -12.04163662
stats
parameter 75% 97.5%
alpha 26.056603972 32.441814713
beta -0.009531957 -0.006216254
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y_pred[2] 5.000000000 8.000000000
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y_pred[5] 5.000000000 8.000000000
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y_pred[42] 3.000000000 6.000000000
y_pred[43] 3.000000000 6.000000000
y_pred[44] 3.000000000 6.000000000
y_pred[45] 3.000000000 6.000000000
y_pred[46] 3.000000000 5.000000000
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y_pred[49] 3.000000000 5.000000000
y_pred[50] 3.000000000 5.000000000
y_pred[51] 3.000000000 5.000000000
y_pred[52] 3.000000000 5.000000000
y_pred[53] 3.000000000 5.000000000
y_pred[54] 3.000000000 5.000000000
y_pred[55] 3.000000000 5.000000000
y_pred[56] 3.000000000 5.000000000
y_pred[57] 2.000000000 5.000000000
y_pred[58] 2.000000000 5.000000000
y_pred[59] 2.000000000 5.000000000
y_pred[60] 2.000000000 5.000000000
y_pred[61] 2.000000000 5.000000000
y_pred[62] 2.000000000 4.000000000
y_pred[63] 2.000000000 5.000000000
y_pred[64] 2.000000000 4.000000000
y_pred[65] 2.000000000 4.000000000
y_pred[66] 2.000000000 4.000000000
y_pred[67] 2.000000000 4.000000000
y_pred[68] 2.000000000 4.000000000
y_pred[69] 2.000000000 4.000000000
y_pred[70] 2.000000000 4.000000000
y_pred[71] 2.000000000 4.000000000
y_pred[72] 2.000000000 4.000000000
y_pred[73] 2.000000000 4.000000000
y_pred[74] 2.000000000 4.000000000
y_pred[75] 2.000000000 4.000000000
y_pred[76] 2.000000000 4.000000000
y_pred[77] 2.000000000 4.000000000
y_pred[78] 2.000000000 4.000000000
y_pred[79] 2.000000000 4.000000000
lp__ -11.621549839 -11.350281393
, , chains = chain:4
stats
parameter mean sd 2.5% 25% 50%
alpha 22.80417187 4.682366625 13.89372617 19.62490452 22.77945018
beta -0.01158021 0.002479939 -0.01639852 -0.01323601 -0.01155781
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y_pred[7] 3.64720000 1.948920680 0.00000000 2.00000000 3.00000000
y_pred[8] 3.60500000 1.943226756 0.00000000 2.00000000 3.00000000
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y_pred[10] 3.51100000 1.899315793 0.00000000 2.00000000 3.00000000
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y_pred[14] 3.33140000 1.852852032 0.00000000 2.00000000 3.00000000
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y_pred[17] 3.19300000 1.783476144 0.00000000 2.00000000 3.00000000
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y_pred[19] 3.15960000 1.770297893 0.00000000 2.00000000 3.00000000
y_pred[20] 2.98700000 1.744545697 0.00000000 2.00000000 3.00000000
y_pred[21] 2.99740000 1.776407714 0.00000000 2.00000000 3.00000000
y_pred[22] 3.04560000 1.750580917 0.00000000 2.00000000 3.00000000
y_pred[23] 2.99820000 1.762276336 0.00000000 2.00000000 3.00000000
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y_pred[25] 2.88600000 1.725919975 0.00000000 2.00000000 3.00000000
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y_pred[73] 1.37460000 1.186489103 0.00000000 0.00000000 1.00000000
y_pred[74] 1.35780000 1.170492704 0.00000000 0.00000000 1.00000000
y_pred[75] 1.31500000 1.179005094 0.00000000 0.00000000 1.00000000
y_pred[76] 1.27760000 1.153431541 0.00000000 0.00000000 1.00000000
y_pred[77] 1.17320000 1.130069543 0.00000000 0.00000000 1.00000000
y_pred[78] 1.13880000 1.074507084 0.00000000 0.00000000 1.00000000
y_pred[79] 1.12020000 1.096354121 0.00000000 0.00000000 1.00000000
lp__ -12.31662538 1.029051463 -15.16789075 -12.66861046 -12.01723170
stats
parameter 75% 97.5%
alpha 25.930141013 31.920646899
beta -0.009908512 -0.006861711
y_pred[1] 5.000000000 8.000000000
y_pred[2] 5.000000000 8.000000000
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y_pred[5] 5.000000000 8.000000000
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y_pred[7] 5.000000000 8.000000000
y_pred[8] 5.000000000 8.000000000
y_pred[9] 5.000000000 8.000000000
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y_pred[27] 4.000000000 6.000000000
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y_pred[31] 4.000000000 6.000000000
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y_pred[35] 3.000000000 6.000000000
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y_pred[77] 2.000000000 4.000000000
y_pred[78] 2.000000000 4.000000000
y_pred[79] 2.000000000 4.000000000
lp__ -11.603849353 -11.345792048
# Extraer las estimaciones de los parámetros <- extract (fit_muertes)<- estimaciones_desastres$ alpha<- estimaciones_desastres$ beta# Extraer las predicciones generadas por el modelo para los años observados <- estimaciones_desastres$ y_pred# Calcular la media y la desviación estándar de las predicciones <- colMeans (y_pred_desastres)<- apply (y_pred_desastres, 2 , sd)# Mostrar los resultados para las predicciones de desastres por año cat ("La media predictiva de desastres por año es:" , mean (mean_pred_desastres), " \n " )
La media predictiva de desastres por año es: 2.418924
cat ("La desviación estándar predictiva de desastres por año es:" , mean (sd_pred_desastres), " \n " )
La desviación estándar predictiva de desastres por año es: 1.55199
Gráficas e interpretación
# Trace plot de las cadenas MCMC para alpha y beta mcmc_trace (as.array (fit_muertes), pars = c ("alpha" , "beta" ))# Densidades posteriores de alpha y beta mcmc_dens_overlay (as.array (fit_muertes), pars = c ("alpha" , "beta" ))# Relación entre año y probabilidad de desastre ggplot (data = data.frame (x = years, y = counts), aes (x = x, y = y)) + geom_point () + stat_smooth (method = "glm" , method.args = list (family = "poisson" ), se = FALSE )
`geom_smooth()` using formula = 'y ~ x'
# Intervalos de credibilidad para alpha y beta mcmc_intervals (as.array (fit_muertes), pars = c ("alpha" , "beta" ))
Basándonos en el modelo estadístico, estimamos que la mina experimenta en promedio 2.42 desastres al año, con una variabilidad típica que podría resultar en un rango de 0.86 a 3.98 desastres en un año dado. Estos números ayudarán a la compañía de seguros a evaluar los riesgos y a planificar adecuadamente sus pólizas y estrategias de mitigación.
alpha :
Valor estimado: 22.92
Intervalo de credibilidad del 95%: [13.23, 32.53]
Interpretación: El parámetro alpha representa el nivel de desastres en la mina cuando todas las demás variables se mantienen constantes. Según el modelo, estimamos que el nivel basal de desastres en la mina es aproximadamente 22.92. Sin embargo, dado el intervalo de credibilidad del 95%, podemos estar aproximadamente 95% seguros de que el verdadero valor de alpha cae en el rango de 13.23, 32.53, lo cual es bastante amplio y refleja la incertidumbre.
beta :
Valor estimado: -0.01
Intervalo de credibilidad del 95%: [-0.02, -0.01]
Interpretación: El parámetro beta representa la relación entre el tiempo (año) y la tasa de desastres en la mina. Según este modelo, estimamos que por cada aumento unitario en el año, la tasa de desastres en la mina disminuye en aproximadamente 0.01 unidades. El intervalo de credibilidad del 95% sugiere que podemos estar aproximadamente 95% seguros de que la verdadera relación entre el tiempo y la tasa de desastres cae en el rango de -0.02 a -0.01.
La media predictiva de desastres por año es: 2.416199
La desviación estándar predictiva de desastres por año es: 1.550927
# PPC # Extraer las muestras de los parámetros del modelo <- extract (fit_muertes)# Definir la función inv_logit <- function (x) {exp (x) / (1 + exp (x))# Generar predicciones posteriores para cada observación <- length (years) # Número de observaciones <- dim (samples$ alpha)[1 ] # Número de muestras en la cadena MCMC <- matrix (NA , nrow = n_obs, ncol = n_samples) # Matriz para almacenar predicciones for (i in 1 : n_samples) {<- samples$ alpha[i] + samples$ beta[i] * years<- rpois (n_obs, exp (mu)) # Muestreo de distribución de Poisson usando la media de mu # Calcular la media de las predicciones <- apply (yrep, 1 , mean)# Calcular los límites del gráfico <- range (c (counts, predicciones_media))<- range (c (counts, predicciones_media))# Crear el gráfico de dispersión con los límites ajustados plot (counts, predicciones_media,xlab = "Valores Observados" ,ylab = "Media de Valores Predichos" ,main = "PPC: Valores Observados vs. Media de Valores Predichos" ,xlim = x_limits,ylim = y_limits)# Añadir una línea roja con pendiente positiva abline (a = 0 , b = 1 , col = "red" )
Observamos que el modelo no se ajusta adecuadamente a los datos. Esto sugiere que el modelo no captura completamente la estructura subyacente de los desastres en la mina a lo largo del tiempo. Es posible que existan otros factores no considerados en el modelo que influyan en la ocurrencia de desastres, o que la relación entre el tiempo y la frecuencia de desastres no sea lineal como se asumió en el modelo.
Inciso ii)
# El parámetro tau es el punto de inflexión que indica el año en el que cambia la tasa de desastres. Antes de este punto, la tasa es determinada por alpha (b0), y después de este punto, la tasa se incrementa en beta (b1). library (rstan)library (boot)# Cargar los datos data (coal)# Convertir las fechas a años completos desde 1851 y contar los desastres por año <- as.integer (floor (coal$ date))<- table (disaster_years)# Generar un vector de todos los años desde el primer hasta el último año registrado <- seq (from = min (disaster_years), to = max (disaster_years))# Inicializar un vector para contar los desastres, llenándolo con ceros para todos los años <- setNames (rep (0 , length (all_years)), all_years)# Actualizar los conteos basados en los desastres registrados names (disaster_counts)] <- as.integer (disaster_counts)# Convertir los conteos a un vector numérico sin nombres <- as.integer (counts_full)# Preparar los datos para Stan incluyendo min_year y max_year <- list (N = length (all_years),disasters = counts,years = as.numeric (names (counts_full)),min_year = as.numeric (min (all_years)), # Añadiendo min_year max_year = as.numeric (max (all_years)) # Añadiendo max_year # Asegúrate de ajustar la ruta al archivo Stan <- "Ej5-modelo3.stan" # Compilar y ajustar el modelo Stan <- stan_model (file = stan_model_path)<- sampling (stan_model, data = stan_data, iter = 10000 , warmup = 5000 , chains = 4 )
SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
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SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
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SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
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Warning: There were 19553 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See
https://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded
Warning: Examine the pairs() plot to diagnose sampling problems
# Imprimir los resultados print (fit)
Inference for Stan model: anon_model.
4 chains, each with iter=10000; warmup=5000; thin=1;
post-warmup draws per chain=5000, total post-warmup draws=20000.
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
beta0 1.14 0.00 0.10 0.94 1.07 1.14 1.20 1.32 830 1
beta1 -1.23 0.01 0.16 -1.53 -1.33 -1.22 -1.12 -0.93 888 1
tau 1890.49 0.08 2.45 1886.15 1889.15 1890.69 1891.78 1896.44 985 1
lp__ -52.58 0.03 1.33 -56.02 -53.17 -52.26 -51.64 -50.92 1954 1
Samples were drawn using NUTS(diag_e) at Sun Mar 17 13:41:26 2024.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at
convergence, Rhat=1).
$summary
mean se_mean sd 2.5% 25% 50%
beta0 1.137130 0.003339836 0.09620865 0.9449748 1.073868 1.138279
beta1 -1.227894 0.005203429 0.15504598 -1.5328288 -1.331788 -1.224919
tau 1890.490814 0.077979534 2.44762142 1886.1502010 1889.149921 1890.685107
lp__ -52.582309 0.030118546 1.33126846 -56.0218961 -53.170964 -52.256975
75% 97.5% n_eff Rhat
beta0 1.202659 1.3229838 829.8088 1.004990
beta1 -1.120500 -0.9321528 887.8543 1.002887
tau 1891.779540 1896.4432010 985.2064 1.001399
lp__ -51.642299 -50.9202836 1953.7243 1.001276
$c_summary
, , chains = chain:1
stats
parameter mean sd 2.5% 25% 50%
beta0 1.125890 0.09541181 0.9275877 1.063588 1.128601
beta1 -1.215192 0.15317930 -1.5206998 -1.315154 -1.211544
tau 1890.588482 2.44874578 1886.1707533 1889.250091 1890.776933
lp__ -52.584476 1.38167342 -56.3268560 -53.152246 -52.225632
stats
parameter 75% 97.5%
beta0 1.191649 1.3045067
beta1 -1.112432 -0.9204617
tau 1891.812235 1896.4810669
lp__ -51.615335 -50.9059227
, , chains = chain:2
stats
parameter mean sd 2.5% 25% 50%
beta0 1.135319 0.09847063 0.927935 1.071463 1.137902
beta1 -1.222211 0.15577064 -1.521014 -1.326764 -1.222809
tau 1890.349316 2.38646266 1886.154663 1889.048578 1890.540380
lp__ -52.594765 1.33067770 -56.029261 -53.176696 -52.255682
stats
parameter 75% 97.5%
beta0 1.201819 1.3239472
beta1 -1.117065 -0.9163291
tau 1891.723355 1896.2771001
lp__ -51.646078 -50.9263593
, , chains = chain:3
stats
parameter mean sd 2.5% 25% 50%
beta0 1.149711 0.08955377 0.9746882 1.088991 1.149426
beta1 -1.244208 0.14971751 -1.5362948 -1.349166 -1.244195
tau 1890.498737 2.35974968 1886.1397598 1889.191488 1890.735420
lp__ -52.517202 1.22098471 -55.5892678 -53.127334 -52.247847
stats
parameter 75% 97.5%
beta0 1.209788 1.3253952
beta1 -1.137004 -0.9685627
tau 1891.807803 1896.1171019
lp__ -51.615856 -50.9070188
, , chains = chain:4
stats
parameter mean sd 2.5% 25% 50%
beta0 1.137602 0.09960948 0.9481158 1.070399 1.136723
beta1 -1.229965 0.15988609 -1.5497242 -1.334760 -1.224349
tau 1890.526722 2.58381508 1886.1295222 1889.115144 1890.660063
lp__ -52.632795 1.38300009 -56.1668227 -53.244609 -52.302362
stats
parameter 75% 97.5%
beta0 1.204941 1.333438
beta1 -1.118363 -0.930754
tau 1891.771993 1896.673267
lp__ -51.686628 -50.940586
beta0 (Intercepto):
Media : La media de beta0tau
Desviación estándar (sd) : Una desviación estándar de 0.096 sugiere una variabilidad moderada en las estimaciones de beta0
IC 95% : El intervalo de credibilidad al 95% va desde aproximadamente 0.945 hasta 1.323, indicando dónde se espera que caiga el verdadero valor de beta0
Convergencia : Un Rhatn_eff
beta1 (Pendiente después del punto de cambio tau):
Media : La media de beta1tau
Desviación estándar (sd) : Una desviación estándar de 0.155 indica una variabilidad moderada en las estimaciones de beta1
IC 95% : El intervalo de credibilidad al 95% va desde aproximadamente -1.533 hasta -0.932, lo cual no cruza cero y sugiere que hay un efecto significativo de la variable tiempo en la tasa de desastres después de tau
Convergencia : El Rhatn_eff
tau (Año de cambio):
Media : La media de tau
Desviación estándar (sd) : Una desviación estándar de 2.448 indica que hay una cierta incertidumbre acerca del año exacto en que ocurrió el cambio, pero esta incertidumbre no es excesivamente grande.
IC 95% : El intervalo de credibilidad al 95% va desde aproximadamente 1886.15 hasta 1896.44, proporcionando una ventana de tiempo dentro de la cual es probable que haya ocurrido el cambio.
Convergencia : Un Rhatn_efftau
mcmc_trace (fit, pars = c ("beta0" , "beta1" , "tau" ))mcmc_areas (fit, pars = c ("beta0" , "beta1" , "tau" ))mcmc_pairs (fit, pars = c ("beta0" , "beta1" , "tau" ))mcmc_acf (fit, pars = c ("beta0" , "beta1" , "tau" ))
Warning: The `facets` argument of `facet_grid()` is deprecated as of ggplot2 2.2.0.
ℹ Please use the `rows` argument instead.
ℹ The deprecated feature was likely used in the bayesplot package.
Please report the issue at <https://github.com/stan-dev/bayesplot/issues/>.
mcmc_intervals (fit, pars = c ("beta0" , "beta1" , "tau" ))
